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LAWS OF WAGES 



THE MACMILLAN COMPANY 

NEW YORK • BOSTON • CHICAGO 
SAN FRANCISCO 

MACMILLAN & CO., Limited 

LONDON • BOMBAY • CALCUTTA 
MELBOURNE 

THE MACMILLAN CO. OF CANADA, Ltd. 

TORONTO 



LAWS OF WAGES 



AN ESSAY IN STATISTICAL ECONOMICS 



BY 



HENRY LUDWELL MOORE 

PROFESSOR OF POLITICAL ECONOMY IN COLUMBIA 
UNIVERSITY 



' ' II progresso dell' Economia politica dipenderk. 
pel futuro in gran parte dalla ricerca di leggi em- 
piriche, ricavate dalla statistica, e che si parago- 
neranno poi colle leggi teoriche note, o che ne 
faranno conoscere di nuove." Pareto. 



THE MACMILLAN COMPANY 
1911 

AU rights reserved 



V 



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COPTEIGIIT, 1911, 

By the M ACM ill an CO. 

Set up and electrotyped. Published December, 1911. 



Nortoooli ^t£ss 

J. S. Gushing Co. — Berwick & Smith Co. 

Norwood, Mass., U.S.A. 



©C1A303503 



TO 

JOHN BATES CLAEK 

IN ADMIRATION AND AFFECTION 
I DEDICATE THIS ESSAY 



CONTENTS 



PAGE 

Introduction 1 



CHAPTER I 

STATISTICAL LAWS 

A Scatter Diagram 11 

Definition of Terms . .15 

Cliaracteristics of Statistical Laws 21 



CHAPTER II 

"WAGES, MEANS OF SUBSISTENCE, AND THE STANDARD 
OF LIFE 

Description of Data , 26 

Wages and the Means of Subsistence 29 

Wages and the Standard of Life 33 

Wages of Skilled and of Unskilled Laborers . . . .39 



CHAPTER III 

WAGES AND THE PRODUCTIVITY OF LABOR 

Description of Data . , . .45 

Fluctuations in the Rate of Wages and in the Value of the 

Product 46 

Fluctuations in the Laborer's Relative Share of the Product and 

in the Ratio of Capital to Labor 55 

The General Trend of Wages 61 

vii 



viii Contents 



CHAPTER IV 

WAGES AND ABILITY 

An Hypothesis as to the Distribution of Ability . 

Grounds for the Hypothesis . 

The Expression of the Gaussian Law in a Form that will facili- 
tate the Testing of the Differential Theory of Wages . 

The Standard Population 

The Application of the Theory of the Standard Population 
Remark upon the Preceding Demonstration 



PAGE 

74 
76 

78 
82 
85 
93 



CHAPTER V 

WAGES AND STRIKES 

Outcome of Strikes as affected by the Strength of Trades-Unions 105 
Outcome of Strikes as limited by Economic Law . . . 121 
Summary 134 

CHAPTER VI 

WAGES AND THE CONCENTRATION OF INDUSTRY 

Wages as affected by the Concentration of Industry . • . 140 

Amount of Employment 153 

Continuity of Employment 156 

Length of the Working Day 161 

CHAPTER VII 

CONCLUSIONS 

Statistical Economics and Industrial Legislation . . . 169 
Practical Aspects of the Results of Preceding Chapters . . 174 
Statistical Economics and Synthetic Economics .... 196 



LAWS OF WAGES 



LAWS OF WAGES 



INTRODUCTION 

Theke are five circumstances tlie coexistence of 
which at the present time will probably determine 
in the near future the direction and character of such 
economic investigations as shall have for their object 
the discovery of general facts and laws : — 

(1) The pure theory of economic statics has 
reached a definite, mathematically symbolic form; 
it supplies a general view of the economic field, 
and indicates the desiderata for further theoretical 
inquiries. 

The utility of economic theory is to be measured 
by the degree in which it solves its triple task of 
definition and analysis of concepts, the discovery of 
appropriate methods for handling mutually dependent 
social phenomena, and the presentation of a general 
view of the economic field. Clearness and precision 
of definition are absolutely indispensable to any form 
of quantitative work. So long as economic terms 
were employed with the vagueness illustrated by 
Jevons when he showed that in the use of the word 
" value " three distinct meanings were habitually 
■ confused, it " was not to be expected that we could 
profitably discuss such matters as economic doc- 



2 Laws of Wages 

trines." ^ The net result of the subtle discrimination 
and criticism of concepts which has characterized 
a great portion of contemporary work is that, for 
the first time, the inductive worker has a choice of 
groups of terms that are precise and clear. 

In a similar manner, in quite recent years, the 
idea of the relations of economic phenomena has 
widened, and methods have been discovered that 
enable us to visualize these interrelations in their 
complexity. Economic events are not arrayed in 
linear connection, the one event following the other 
in direct series, as was frequently assumed by the 
classical economists. It was an idle controversy that 
Malthus and Ricardo conducted upon the question 
whether the abundance of food increases the popula- 
tion or the multitude of consumers increases the 
supply of food. Social phenomena are interrelated, 
are mutually dependent, and the appropriate method 
of treating such a form of interdependence is the use 
of a system of simultaneous equations in which the 
equations are equal in number to the unknown quan- 
tities in the problem. There are hints of this con- 
ception in the works of the earlier economists; for 
exan.ple, in Cournot's RecliercJies sur les princiijes 
mathematiques de la theorie des richesses, but it was 
missed by Jevons, as was shown by Professor Marshall 
in his Academy review of Jevons's TJieory of Political 
Economy. Walras introduced it in an important 
special case in his earlier treatise. It has received 

^ W. S. Jevons : The Theory of Political Economy, 3d edition, p. 81. 



Introduction 3 

its complete development in Professor Marshall's 
Principles of Economics and Professor Pareto's Cours 
d' economic politique. 

The third part of the task of the economic theory 
— the presentation of a general view of the economic 
field — was achieved in the perfection of the method 
of simultaneous equations which has just been de- 
scribed. In a non-symbolic form, the general survey 
was made in the original treatise of Professor J. B. 
Clark. 

(2) Marxian socialists have distinguished between 
the constructive and the destructive elements of their 
prophet's teachings, and are seeking to extend the 
theory of socialism through the development of the 
constructive idea in the light of concrete data. 
The real beginning of a "scientific socialism" was 
in Bernstein's confession : " Die Fortentwicklung und 
Ausbildung der marxistischen Lehre muss mit ihrer 
Kritik beginnen. Heute steht es so, dass man aus 
Marx und Engels alles beweisen kann."-^ It was a 
considerable step toward "industrial emancipation" 
for leading socialists like Bernstein and Sorel to 
recognize the vagueness, inconsistency, and inade- 
quacy of Marx's teachings ; it was a greater stride 
in the same direction to face the necessity of attack- 
ing anew the old problems and to decide to conduct 
further inquiries upon the basis of concrete facts. 
The newer " scientific socialism " will rest upon 

^ Ed. Bernstein: Die Voraussetzungen des Sozialismus und die Auf- 
gaben der Sozialdemokratie, p. 19. 



4 Laws of Wages 

formulae derived from experience : " Je propose de 
nommer economie concrete la science moderne qui se 
fonde, a la fois sur I'observation directe des faits et 
sur la connaissance des theories abstraites qui lui 
permettent de comprendre I'emploi que Ton pent faire 
des concepts."^ The aim of modern theoretical so- 
cialism thus described by Sorel is the aim of modern 
economics. 

(3) The growth of social democracy has led to 
measures of industrial reform whose administration 
requires the periodic collection of varied statistics 
upon a large scale. Reforms in measures of taxation, 
where the reforms are genuine, now, for the first 
time, give a definite idea as to the amount of the 
wealth of nations and its yield of earned and un- 
earned incomes. Reforms in the character of indus- 
trial insurance and in government reports as to the 
condition of labor now give detailed information as 
to the distribution of wages, the cost of living among 
laborers, the causes and seasons of unemployment, 
the relative frequencies and causes of industrial dis- 
putes, the prevalence of diseases among workers, and 
the disabilities of old age. The material for the 
concrete treatment of economic questions is being 
supplied yearly in increasing abundance. 

(4) The problems of natural science have required 
the invention of a calculus of mass phenomena that 
will probably yield its best results when applied to 
the material of the social sciences. The wealth of 

^ Georges Sorel : Introduction a Vdconomie moderne, p. 28. 



Introduction 5 

the statistical material relating to economic questions 
is itself a source of embarrassment. To utilize it 
for scientific purposes, it must be described in brief, 
summary formul£e, and these formulae must be 
arranged upon a plan of increasing complexity so 
that it will be possible to pass from accurate descrip- 
tions of mass aggregates to the relations between 
the aggregates themselves. Now, concurrently with 
the development of economic and socialistic theory 
and the increasing supply of statistical data, the 
mathematical instrument for rendering the statistical 
data available for scientific purposes has been per- 
fected. The calculus of mass phenomena, like the 
infinitesimal calculus, owes its development to many 
workers, but, in recent years, its efficiency has been 
increased by the labors of Professor Pearson and 
Professor Edgeworth far more than during the whole 
period intervening since the days of Laplace and 
Gauss. There is reason for believing that, as the 
science of statistics had its origin in the treatment 
of social questions, so likewise the newer statistical 
methods will yield their most important results when 
applied to social data. 

(5) The perfection of mechanical devices for per- 
forming mathematical computations has rendered it 
possible for individual scientists to elaborate the new 
data supplied by government bureaus. When a 
science is in its early stages, individual scientists 
must do work of many kinds. For some years to 
come all essays in the direction of connecting economic 



6 Laws of Wages 

theory with economic practice must be tentative, for 
the investigator must at the same time master the 
theory, collect the facts, and take from them their 
content by means of new and difficult methods. 
With the mass of data before him, the task would 
be impossible without mechanical aids to computa- 
tion. These aids are being supplied in increasing 
numbers and value in the form of mathematical 
tables, mechanical tabulators, and arithmometers. 

In the following chapters I have endeavored to 
use the newer statistical methods and the more 
recent economic theory to extract, from data re- 
lating to wages, either new truth or else truth in 
such new form as will admit of its being brought 
into fruitful relation with the generalizations of 
economic science. 

The first chapter contains a description of the 
meaning of the terms representative fact, hypothesis, 
statistical law, which are the principal categories by 
means of which scientific results are classified. In 
order to secure a wise expenditure of capital and 
energy, it is necessary in economic science as in 
economic affairs to make, from time to time, an 
inventory of one's possessions, and to this end it is 
all important that there should be no ambiguity 
about the table of values by means of which the 
inventory is effected. In particular, we economists 
should recognize the truth that, throughout a very 



Introduction 7 

long period of its history, our science has been con- 
cerned with hypotheses while it has pretended to the 
discovery of laws. 

Having defined our terms and illustrated our 
method, we pass to the consideration of economic 
theories of wages in the light of existing data relat- 
ing to the income of laborers. The persistence in 
economic speculation of the doctrines of wages that 
are associated with the names, respectively, of Turgot 
and Ricardo requires that the statistical economist 
should measure, if he can, the degree of truth con- 
stained in each theory. Data are now available, per- 
haps for the first time, upon which to base an 
inductive investigation. This material is utilized 
to measure the degree of relation between wages and 
the cost of the means of subsistence, and between 
wages and the standard of life of the laborer. 

The theory according to which, under perfect com- 
petition, the laborer tends to receive as wages the 
value of his specific product is one phase of a general 
theory of distribution that owes its development to 
contemporary economists. It will not be denied, 
I think, that one's attitude toward theoretical eco- 
nomics and industrial reform should be greatly affected 
by the outcome of an inductive test applied to this 
doctrine. The theory contains two principal parts : 
(1) as to the trend of the share of the product that 
goes to the whole class of laborers in the form of 
general wages, and (2) as to the law of the distri- 
bution of general wages among the subgroups form- 



8 Laws of Wages 

ing the laboring class. These two parts of the 
productivity theory of wages I have subjected to 
statistical treatment. 

Owing to the fact that the productivity theory 
was developed by economists who employed the 
device of a static state to facilitate the working of 
their isolated hypotheses, it has been assumed by 
sympathetic critics that its validity is limited to a 
hypothetical static state. This criticism must be 
withdrawn if it can be shown that the theory sup- 
plies the clue to the explanation of a concrete, highly 
dynamic phenomenon of the first importance. What 
light can the productivity theory of wages throw 
upon the scientific problem of the economic laws 
of strikes and their outcome ? To answer this ques- 
tion the first obvious desideratum is the proof that 
strikes and their outcome are subject to law ; it will 
then be time to inquire whether the observed regu- 
larities are explicable by means of the productivity 
hypothesis. 

Of at least equal importance with the question of 
the relation of strikes to wages is the consideration 
of the effects upon the condition of the laborers of 
the concentration of industry in large establishments. 
It will be shown, for example, that the mean rate 
of wages in the textile industries tends to increase 
with the size of the establishment. But what shall 
be the interpretation of this result ? Shall the infer- 
ence be that the more highly organized technical 
equipment of the larger establishments results in a 



Introduction 9 

higher effective productivity of the laborer, which 
finds its expression in a larger wage? Or may it 
not be that the great industrial machines select the 
ablest laborers at the age when they are most pro- 
ductive, and then, after the very best of their lives 
has been exploited, throw them out of the industry 
to find their support elsewhere? The law of the 
variation of wages with age, in the general industry 
and in the large establishments, will give light upon 
this problem. The high mean wages of large estab- 
lishments may be spurious averages due to the differ- 
ent ages of the populations in large and in small 
establishments. The real social gain or loss resulting 
from the concentration of industry can be measured 
only after the consequences have been apprehended 
of the selective process that concentration entails. 

In a concluding chapter, the general results of the 
essay are summarized with the purpose of consider- 
ing their bearing upon the problem of the organiza- 
tion of industry. It is hoped that, supported as they 
are by economic theory and inductive verification, 
they may, in their degree, add to the positive knowl- 
edge that shall be utilized in the control of the eco- 
nomic changes that follow upon our increasing wealth 
and population. 



CHAPTER I 

STATISTICAL LAWS 

" En general, une theorie scientifique quelconque, imaginee pour 
relier un certain nombre de faits trouves par I'observation, peut etre 
assimile'e k la courbe que Ton trace d'apres une ddfinition mathe'ma- 
tique, en s'imposant la condition de la faire passer par un certain 
nombre de points donnds d'avance. Le jugenient que la raison porte 
sur la valeur intrinseque de cette the'orie est un jugenient probable, 
dont la probabilite tient d'une part a la simplicite de la formula 
th^orique, d'autre part au nombre des faits ou des groupes de faits 
qu'elle relie." _ Cournot. 

The statistical economist is concerned with eco- 
nomic facts, hypotheses, and laws. He begins his 
investigations with the assembling of facts, and seeks 
through the mediation of hypotheses to arrive at 
laws. As economist, his aim is to throw the great- 
est possible light upon the relation of the economic 
facts before him, and, as scientist, he expects to 
achieve this end by summarizhig the descriptions of 
the relations of facts in the simplest and most gen- 
eral formulae possible. Equipped with new and 
powerful instruments of research, he approaches his 
task in a precise, systematic way that yields results 
in a much more definite and usable form than the 
inspiring generalizations of the early masters of the 
science. 

What, precisely, was the meaning of Adam Smith in 

10 



Statistical Laws 11 

his eniimeration of the following circumstances in con- 
nection with the discussion of the inequalities in wages ? 
" First, the agreeableness or disagreeableness of the 
employments themselves; secondly, the easiness and 
cheapness, or the difficulty and expense of learning 
them ; thirdly, the constancy or inconstancy of employ- 
ment in them ; fourthly, the small or great trust which 
must be reposed in those who exercise them ; and fifthly, 
the probability or improbability of success in them." 
Did he mean that these factors are always present as 
causes of inequalities in wages, that they are of equal im- 
portance, and that wages vary in either direct or inverse 
ratio with their several variations? Or, was not his 
meaning, rather, that the enumerated factors are so many 
possible hypotheses, one or more of which, in particular 
cases, may give the clue to the observed inequality in 
wages ? Before it would be allowable to speak of a law 
of wages, in any particular case, it would be necessary to 
show not only that wages vary with the assumed factor, 
but to derive the formula of the variation and to meas- 
ure the degree of association between the phenomena. 
It will contribute to the better understanding of 
the nature of the results in subsequent chapters to 
consider here the meaning of the terms : general or 
representative fact, hypothesis, statistical law. 

In the accompanying Figure 1 the details of a 
" scatter diagram " ^ are depicted. A scatter diagram 
is a graphic description of the quantitative relation 

1 A term due to Professor Pearson. 



12 



Laws of Wages 







Statistical Laws 



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14 Laws of Wages 

between two series of facts. In this particular case 
the two groups of facts are the average wages of men 
and the average wages of women, in the several states 
and territories of the United States.^ The scatter 
diagram is constructed by measuring in sequence 
upon the horizontal line the tabular values, for the 
several states and territories, of the average wages of 
men, and then plotting perpendicularly to these values 
the corresponding average wages of women. Each 
pair of related values is represented by a point upon 
the diagram. For example, in case of Montana, 
the average wage of men was $18.60 a week, and the 
corresponding wage for women was $8.60. This 
relation is indicated by the extreme point in the 
upper right-hand corner of the diagram. 

The next stage in the construction of the scatter 
diagram is represented by the series of small circles 
that are connected by a broken line. The facts upon 
which this part of the construction rests are given in 
Table I. The individual observations are not dealt 
with directly as they are indicated upon the diagram, 
but they are grouped into arrays the characteristics 
of which are summarized in averages and then repre- 
sented upon the diagram by circles. For example, 
in the states in which the average wages of men were 
between $10 and $11 a week, the corresponding 
wages of women formed an array whose average 
value was $5.60. This representative value of the 

1 The data are taken from the Census of Manufactures, 190.5, 
Bulletin 93, p. 36. 



Statistical Laws 15 

array is indicated by the circle placed above the point 
$10.50, at a distance from the horizontal line corre- 
sponding to $5.60 on the perpendicular scale. The 
circles are connected by a broken line. 

Suppose, now, that the particular problem to be 
investigated is the relation between the wages of men 
and the wages of women. From the general sweep 
of the scatter diagram one would say that the two 
quantities are related. But what is the exact nature 
of the function descriptive of the relation, and what 
is the degree of association between the wages of men 
and the wages of women ? The attempt to give 
definite answers to these questions will lead to a 
specific instance of the exact use of the terms : gen- 
eral fact, hypothesis, statistical law. 

The series of points upon the scatter diagram is 
simply a graphical transcript of a double entry table 
recording the series of related measurements. But 
where the observations mount into hundreds and 
thousands, it would be extremely laborious to consider 
directly the more or less accidental position of each 
point, and still, in giving a summary description of 
the relation of two series of values — which is the 
object of the investigation — it is not allowable to 
neglect the singularity of any point. Each point 
must have a weight in the investigation that is pro- 
portional to its importance. 

Now, in any investigation, the general, or represen- 
tative, fact is that fact which for the purpose in hand 
conveys the maximum of information about the group 



16 Laws of Wages 

it represents. In the problem before us, the arith- 
metical averages ^ of the items in the several arrays 
are regarded as representative of their respective 
groups. By substituting representative observations 
for the individual observations, the number of points 
to be treated, in the case under consideration, is 
reduced from fifty to twelve. 

What is the law of the association of the represent- 
ative points? The answer to that question is depend- 
ent upon the finding of the simplest curve that will 
fit satisfactorily the given representative points. An 
hypothesis must be made as to the nature of the 
curve that will satisfy the imposed conditions of 
simplicity and excellence of fit, and the hypothesis 
must then be tested by the representative facts. 
Until this test has been applied, there is no ground 
of preference for any particular hypothesis over an 
infinite number of other possible suppositions as to the 
relation of the series of phenomena under observation. 

Incidentally it may be observed that the ideas 
"simplicity" and " excellence of fit" do not admit of 
rigid general definition. According to the point of 
view, a given curve may be either simple or complex: 
its formula may, for example, have few constants 
and for that reason be regarded as simple, but the 
computation of the constants may involve the use of 
extremely intricate processes, which would more than 
offset the simplicity due to the small number of 

1 For certain classes of problems it might be desirable to use other 
forms of representative values,f or example, the mode or median of arrays. 



Statistical Laws 17 

constants. A particular curve may be regarded as 
simple and appropriate to given conditions because 
of its consonance with a priori theory, or its sim- 
plicity may rest entirely upon the facility with which 
it lends itself to analytical treatment. Similar obser- 
vations maybe made with regard to the idea of excel- 
lence of fit.^ 

Returning to the problem of the quantitative relation 
between the wages of men and the wages of women, 
we inquire whether the straight line upon the scatter 
diagram or some other curve not appearing upon the 
chart is the law of the relation between the wages of 
men and the wages of women. The query leads to 
the definition of the term statistical law. The statis- 
tical law of the association of two series of facts is 
the hypothesis that satisfies best the imposed condi- 
tions of simplicity and excellence of fit to the repre- 
sentative facts. The straight line in the scatter diagram, 
the equation to which is ?/ = .3829 x -h 1.5204, satisfies 
the Pearsonian test ^ of excellence of fit, and is there- 
fore regarded as the statistical law of the association 
of the money wages of men and the money wages of 
women. It may be said definitely that on the average, 
in the case before us, a variation of one dollar in the 
wages of men is associated with a variation of about 
38 cents in the wages of women. 

1 A more detailed discussion of these ideas is given in the article 
" The Statistical Complement of Pure Economics." Quarterly Journal 
of Economics, November, 1908. 

2 Philoaophical Magazine, July, 1900, pp. 157-175. Biometrika, 1902, 
pp. 155-163. 



18 Laws of Wages 

What is the measure of the degree of association 
between the money wages of men and the money 
wages of women ? The above formula, as we have 
observed, conveys the information that upon the 
average a variation of one dollar in the wages of 
men is associated with a variation of about 38 cents 
in the wages of women. But does a variation of 38 
cents in the wages of women bear the same propor- 
tion to the total variation of the wages of women 
that a variation of one dollar in the wages of men 
bears to the total variation of the wages of men ? 
In order that an abstract number expressing the 
measure of correlation between the two series of facts 
may be obtained, the associated variations must be 
expressed in terms of units that measure the respec- 
tive variabilities of the two groups of facts. 

The law of the associated variation is ?/= .3829 x + 
1.5204, where the origin of the coordinates is at 
zero. If the origin be transferred to the mean of the 
system of points, that is, to the point the coordinates 
of which are the mean of the wages of men and the 
mean of the wages of women, the equation becomes 
?/=.3829x. If, now, the standard deviation of the 
wages of men be represented by a-^, and the standard 
deviation of the wages of women, by cts, the equation 

may be written y = r — x, or -^ =r — , where r, 

which is the coefficient of correlation, measures 
the degree of association between the variation in 
the money wages of men and the money wages of 



Statistical Laws 19 

women, the variations being expressed in terms of 
the standard deviations of the respective groups. 
But, in the particular case before us, 

r^ = .3829 and o-i = 2.6915, 0-2=1.1898. 

Therefore r= f ^^^^ (.3829) = .866. 

1.1898 

The coefficient of correlation varies between the 
limits ±1. When r= ±1, the correlation between 
the associated variations of the phenomena is per- 
fect. When r=o, there is no linear correlation. 
Intermediate values of r express the degrees of asso- 
ciation between the series of phenomena. 

Inasmuch as the coefficient of correlation, r, is an 
abstract number that is independent of the concrete 
units in which the phenomena are expressed, it makes 
possible the comparison of the degree of association 
between series of phenomena that are qualitatively 
different. For example, it may be proved that the 
wages of skilled laborers vary with the wages of 
unskilled laborers, and it may likewise be shown 
that the wages of skilled laborers vary with their 
standard of life. But in each case, what is the law 
of variation and what is the degree of association 
between the two variables ? Are the w^ages of skilled 
laborers more closely connected with the wages of 
unskilled laborers than with their own standard of 
life ? The appropriate coefficients of correlation give 
the answers to these questions^ as we shall see, in the 
next chapter. 



20 Laws of Wages 

We have no^v a very concrete and detinite idea of 
representative, general facts, liypotlieses, and statistical 
laws. By a progressive synthesis a statistical investi- 
gation passes from individual observations to represent- 
ative facts and from representative facts to statistical 
laws. The representative facts exhibit the charac- 
teristics of the individual observations which, for the 
pm'pose in hand, are most nseful. The statistical 
law summarizes in the simplest possible formula the 
information conveyed by the representative fact«. 

The meanings of these terms in the theorv of statis- 
tics have a general resemblance to their usage in the 
other sciences. For. a theorv or hypothesis as to the 
association of given facts, in any department of 
knowledge, may be likened to an hypi^thesis as to the 
simplest form of curve that will pass as nearly as 
possible to given points. In each case the individual 
observations — the facts and the points — fall into 
groups that may be described by typical, representa- 
tive facts. The hypothesis or theor>' in each case 
is the supposition as to the nature of the relation 
of the representative facts. The law of the facts 
and of the points is the supposition that satisfies 
best the accepted standard of simplicity and ex- 
cellence of lit of the facts to the hypothesis. Before 
any theory is accepted as the appropriate explana- 
tion of the phenomena, proof nnist be submitted 
that the facts which it purports to describe are 
representative facts and that it satisfies the approved 



Statistical Lavjs 21 

test of nirnplicity and excellence of fit to the general 
facts. 

But added to the common idea in the general use 
of these terms, th(3re are special characteristics in 
case of statistical laws that must be discriminated. 
The inductive laws that are established by means of 
statistical methods in the social sciences are — 

(1) Laws of mass phenomena. 

In order to arrive at the conception of statis- 
tical law that has been described in this 
chapter, we summarized the characteristics 
of groups of phenomena by means of repre- 
sentative facts, and then proceeded to test 
the hypothesis as to the relation of the 
general facts by means of a conventional 
standard of simplicity and excellence of fit. 
As the test is applied with reference to the 
general facts, the law is, in reality, the law 
of the general facts : its validity is limited 
to the general facts and need not apply to 
the particular instances. For example, a 
knowledge of the law of mortality will not 
enable one to predict that X, aged forty 
years, will die in a given year. The law, 
however, does yield the necessary information 
for predicting the average proportion of those 
now living who will die in successive years. 

(2) Laws the strict validity of which is limited to 

a particular time and place. 



22 Laws of Wages 

A statistical social law is a summary descrip- 
tion of the resultant of many independent 
factors whose combination varies in time 
and place. The statistical law of the varia- 
tions of price with the supply of a com- 
modity has one form in a highly competitive 
center and quite a different form in an agri- 
cultural community. 
y< (3) Laws the strict validity of which does not ex- 
s< tend beyond the limits of observation. 

A statistical law of inheritance derived from 
the investigation of a population varying 
between the normal limits should not be 
assumed to apply to dwarfs and giants. 
(4) Laws the generality of which ranges from an 
empirical summary of the quantitative rela- 
tion between series of facts of a particular 
time and place to an inductive verification 
of a general theorem of a jyTiori science. 

It would be easy to establish that, in a partic- 
ular country, at a given time, the average 
wage of laborers varies in direct relation 
with the density of the population. But 
such a law of association is simply an em- 
pirical law. If we extended our investiga- 
tion to different times and places, we should 
expect to find a great variation in the de- 
grees of association of the two phenomena. 
But suppose that the productivity theory of 
wages should receive inductive verification 



Statistical Laws 23 

in a particular instance. In that case the 
confidence in the generality and the stability 
of the results would be far greater because 
of the added weight of the a priori demon- 
stration. 

It has been frequently assumed, even by econo- 
mists, that pure economics, concerned as it is with 
general theories, can have but scant relation to the 
varying succession of particular instances of concrete 
life. And, indeed, it is sometimes regarded as futile 
to attempt to bring the two into factual relation. 
But there can be little doubt that the despairing note 
is due to our ignorance of the empirical laws that 
bind together the whole social organism. A definite 
conception of the character and strength of these 
binding ties must lead to a perception of the direct 
connection between pure theory and concrete life. 

Statistical economics, in which the following 
chapters are essays, proposes this twofold object: 
(1) to bring to the test of representative facts the 
hypotheses and theorems of pure economics ; (2) to 
supply data, in the form of general facts and empiri- 
cal laws, for the elaboration of dynamic economics. 



CHAPTER II 

WAGES, MEANS OF SUBSISTENCE AND THE STAND- 
ARD OF LIFE 

" The natural price of labour, therefore, depends on the price of 
the food, necessaries, and conveniences required for the support of 
the labourer and his family." " It is not to be u.nderstood that the 
natural price of labour, estimated even in food and necessaries, is 
absolutely fixed and constant. It varies at different times in the 
same country, and very materially differs in different countries." 

— RiCARDO. 

Three aspects of the remuneration of labor have 
each, at different times, so engaged the attention 
of economists as to lead to three different theories 
of wages : the theory of the dependence of wages 
upon the means of subsistence; the theory of their 
dependence upon the standard of life ; and the theory 
of their dependence upon the laborer's economic pro- 
ductivity. The special conditions of the times in 
which these hypotheses had their origin were doubt- 
less responsible for the distorted perspective exhibited 
in the various attempts to state a scientific theory 
of the laborer's income. In recent years there has 
been a disposition to recognize that each of the 
partial sketches contains an element of truth, but the 
degree of truth in each has not been measured, and 
consequently it has not been possible to weave into a 
satisfactory whole the elements supplied by the 
several theories. 

24 



Means of Subsistence and the Standard of Life 25 

" The general tendency of wages since the intro- 
duction of power machinery and the employment 
of women and children in its operation has been 
upward, but it will be difficult to decide positively 
whether such increase is due absolutely to the use 
of machinery or to a higher standard of living, or 
to the increased productivity of labor supplemented 
by machinery, or to all these causes combined, or to 
other causes. . . . This phase of the subject there- 
fore involves too much speculation for a thoroughly 
statistical presentation ; the method can be only 
suggestive of the arguments which might be used 
for or against the use of machinery because of its 
effect on wages." -^ 

To accept this view of the problem of wages and 
of the limitations of the statistical method would 
be to abandon the hope of solving one of the most 
important problems of industrial life. Indeed, if 
the power of the statistical calculus does not suffice 
to analyze this problem into its constituent elements, 
then all effort in the direction of a concrete science 
of economics is vain ; for all the fundamental prob- 
lems of the science present similar degrees of com- 
plexity. 

Instead of seeking a unique solution of the wages 
question in an a priori way, we shall approach the 
concrete problem by attempting to find statistical 
answers to several important questions related to 

1 Thirteenth Annual Report of the Commissioner of Labor, for the 
United States, 1898, Vol. 1, p. 5. 



26 Laws of Wages 

the subject of this chapter. In the following chap- 
ters other aspects of the problem will be investigated. 
Do wages vary with the cost of the means of 
subsistence, and, if so, what is the law of the vari- 
ation and what is the measure of the correlation in 
the variation ? Do wages vary with the standard 
of life, and, if so, what is the law of the variation 
and the degree of the correlation ? Are wages more 
directly affected by the cost of the means of sub- 
sistence than by the standard of life ? Do the 
answers to these questions differ according as the 
waojes of skilled or of unskilled labor are under 
investigation ? Is there any relation between the 
variation of the wages of skilled labor and the wages 
of unskilled labor ? If there is such a relation, how 
does the degree of correlation compare with the 
correlation of wages with the cost of the means of 
subsistence and with the standard of life ? These 
are some of the very critical questions affecting the 
theory of wages that need to be treated in an induc- 
tive way. 

Description of Data. 

Table I, in the Appendix to this chapter, embodies a 
valuable collection of material relating to the means 
of subsistence, the standard of life and wages. It is 
drawn from the monumental report on Salaires et 
diiree du travail dans V Industrie frangaise which was 
published, in 1893-1897, by the French Office du 
Travail. It has the advantage of having been col- 



Means of Subsistence and the Standard of Life 27 

lected and compiled by a single authority and of 
covering 87 separate departements, thus insuring, 
through the method and simultaneity of the collection 
of data, an unusual comparability of results, and, 
through the scope of the investigation, an adequacy 
of material for scientific generalization. 

In column I, the 87 departemients of France are 
enumerated. In columns II and III, the mean wages 
respectively of unskilled and of skilled laborers are 
given. The raw material upon which the means are 
based was obtained from the conseils de prud'hommes, 
in 1896. The means given for wianceuvres, or unskilled 
laborers, are derived from the wages of journaliers and 
terrassiers, and the means for skilled laborers (I'ouvrier 
de 7netier ordinaire) are the averages for the following 
trades : compositeur d' imprimerie, cordonnier, tailleurs 
d' habits, charron, marechal /errant, plombier, magon} 

In column IV is tabulated for each dejmrtement a 
" coejjicient de depense en objets d' alimentation et 
de chauff age, "which will be referred to, in the argument 
later on, as the cost of the means of subsistence. The 
figure given, in case of each departement, represents 
the cost in that departement of definite quantities of 
selected commodities that are regarded as sufficient to 
sustain, for one year, a family of six members three 
of whom, on the average, are at work. The prices 
that enter into the estimate of the costs are wholesale 
prices that were paid in the respective dep)artements, in 

1 Salaires et dure'e du travail dans Vindustrie franqaise, Vol. IV, pp. 
225, 239, 240. 



28 Laws of Wages 

1893, by representative institutions, such as schools 
and hospitals. The kinds of commodities making up 
the laborer's budget were selected by the Office du 
Travail after having examined the series of index 
numbers previously used in other investigations in 
France. An actual record of expenditures by 14 
families of weavers, composed of six members three 
of whom, on the average, were at work, formed the 
basis for the estimate as to the portions in which the 
several commodities should enter into the index 
number. It is to these weaver budgets that reference 
is made in the French report as to the principles that 
were followed in composing the standard : " nous pren- 
drons simplement pour base de la depense, en ohjets 
d' alimentation, des quantites exprimees en chiffres ronds, 
de telle maniere: (1) que ces quantites soient effectivement 
capahles d' assurer r existence de 6 persoimes, par exam- 
ple ; (2) que la repartition de la depense qui en resulte 
ne secarte pas trop de celle rapportee ci-dessus" ^ 

The figures in column IV represent, therefore, the 
relative costs in the several departements of fixed 
means of subsistence.^ 

^ Salaires et dure'e du travail dans V Industrie fran<;aise, Vol. IV, p. 251. 

2 The kinds and quantities of the commodities are tabulated in 
Vol. IV, p. 252. 

In criticism of this standard budget, it may, of course, be objected 
that retail, instead of wholesale, prices should have been used. But 
the Office du Travail resorted to the use of wholesale figures only after 
the failure of the attempt to secure satisfactory retail prices. Besides, 
the wholesale figures were regarded by the Office du Travail as being 
fairly representative of the local variations of retail prices in France. 

It is to be regretted that an error of unknown magnitude was in- 
troduced in the effort to compensate for the relatively low wholesale 



Means of Subsistence and the Standard of Life 29 

Column V contains for each dejMrtement, the daily 
^^ prix ordinaire de pension pay e par Vouvrier isolej^our 
le logeTnejit et lanourriture." In the subsequent argu- 
ment, this column will be referred to as being repre- 
sentative of the cost of the standard of life.^ Column 
V differs from column IV in that the prix de pension 
is representative of a standard that varies in kind 
and quantity, as v^ell as in prices, from departement to 
departement, v^hile column IV simply records the de- 
partmental prices of a fixed mode of subsistence. 
The figures were obtained, in 1896, from the conseils 
de prudliommes? 

With this description of our data, w^e may now 
enter upon an investigation of the interdependence 
of the several factors that have been described. 

Wages and the Means of Subsistence. 

In its crassest form the doctrine that wages are de- 
termined by the means of subsistence of the laborer 
was formulated by Turgot. " En tout genre de travail 

prices by increasing the quantities of commodities. " Comme les prix 
qui servent de base aux calculs ci-apres sont desprixde gros,nous avons ades- 
sein plutot force les qunntites a multiplier par ces prix, de telle fa(; on que 
les produits representent, aussi approximativement que possible, la depense 
ordinaire d'une famille ouvriere, du type observe, qui ach'ete au detail les 
objets ne'cessaires a l' alimentation et au chauffage." — Vol. IV, pp. 252-253. 

^ I think I am aware of the criticisms that may be urged against 
the assumption that the varying prix de pension is representative of 
the varying standard of life. My study is intended as a first approxi- 
mation, and I hope that judgment will be suspended until the argu- 
ment of the chapter is completed. 

^Ibid., Vol. IV, pp. 244-245, 257-258. 



30 Laws of Wages 

il doit arriver et il arrive en effet que le salaire de 
Vouvrier se home a ce qui lui est necessaire pour lui 
procurer sa subsistance."^ 

If this doctrine has any relevancy to the conditions 
of France to-day, one would say, a 2^riori, that the 
wages of unskilled laborers must be in close associa- 
tion with the cost of the means of subsistence. If 
the relation between the two is one of cause and effect, 
that is to say, if the wages of unskilled laborers are 
determined by the means of subsistence, then the de- 
gree of association must approach unity. These corol- 
laries of the Turgot doctrine may be tested by means 
of columns II and IV of Table I. 

Turgot's doctrine relates to real wages. Column 
IV, as we have seen, is the cost in the different de- 
par tements of a fixed mode of life that approaches the 
necessary means of subsistence of a laborer's family. 
If the relation between means of subsistence and 
the wages of unskilled laborers is a relation of cause 
and effect, then the money wages of unskilled laborers 
in the several departements should be closely correlated 
with the corresponding prices of the means of subsist- 
ence in the departements. 

How close is the association actually found to be ? 
The graph showing the relation between the variation 
in the cost of subsistence and the wages of unskilled 
laborers is given in Figure 2. The law of the asso- 
ciated variation of wages with the cost of subsistence 
is the equation to the straight line, namely, ?/= .864 

^ Turgot : Re'Jlexioyis sur la formation et la distribution ties richesses. 



Means of Subsistence and the Standard of Life 31 




■o 


^ 


o> 


<0 


<») 


^ 


«<5 


^ 


^ 


CV 



£-j9JO(7e/ pa///Majn JO ^a^Pyif 



32 Laws of Wages 

+ .0014 X. The coefficient of correlation is r=.306. 
If we agree to regard values of r less than .25 as 
indicating low correlation ; between .25 — .50, as 
fair correlation; .50 — .75, as high correlation; and 
.75— 1.00, as very high correlation, then, we may say 
that the correlation between the wages of unskilled 
laborers and the means of subsistence, as tested by 
the official data for France, is only fair. We do not 
overlook the facts that the computation of column 
IV presented very great difficulties, and that if rent, 
properly estimated, had been included and the re- 
maining figures had been more accurately determined, 
a closer relation might have been discovered. 

The hypothesis of the causal relation between the 
means of subsistence and the wages of unskilled 
laborers may be tested. If the relation between the 
two were a relation of cause and effect, then ?' should 
approach unity. ^ It is found, however, that the 
actual value of r is .306 ±.066. When the probable 
error of r is considered, it is seen that, if the means 
of subsistence and the wages of unskilled laborers 
were in' causal relation, such a deviation of r from 
unity as ^306 would be practically impossible. 

So far as the data under investigation represent the 
conditions of France to-day, it may be said — 

(1) that the wages of unskilled laborers vary in 
the same direction as the cost of the means 
of subsistence ; 

^ Pearson : Grammar of Science, 2d edit., p. 397. 



Means of Subsistence and the Standard of Life 33 

(2) that the law of the association of the wages of 

unskilled laborers and the means of sub- 
sistence is linear ; 

(3) that the value of the coefficient of correlation 

is r= .306. ±.066, 

(4) that there is no relation of cause and effect 

between the two. 

These conclusions are based upon the data for all 
of the 87 departements of France, excepting the Seine 
and Rliin (Ilaut). For the latter, no record is avail- 
able in case of column lY. The Seine, being the 
departement of Paris, presents anomalous conditions. 

Wages and the Standard of Life. 

Despite Lassalle's intrepretation of Ricardo, the 
classic theory of the relation of wages to the standard 
of life is found in Ricardo's chapter, " On Wages." 

" The natural price of labour . . . depends on the price of 
the food, necessaries and conveniences required for the support 
of the labourer and his family." " It is not to be understood 
that the natural price of labour, estimated even in food and 
necessaries, is absolutely constant. It varies at different times 
in the same country and very materially differs in different 
countries." ^ 

The thesis is that the standard of life varies in time 
and in place and that the wages of laborers vary 
pari passu. The phases of the doctrine relating to 
local variations will be subjected to a test. 

^ Ricardo : Principles of Political Economy and Taxation. McCulloch's 
edition, pp. 50, 52. 



34 Laivs of Wages 

Do the wages of unskilled laborers in France vary 
with the local variations in the standard of life ? If 
a concomitant variation does exist, what is the meas- 
ure of the degree of association between the variables ? 
An approximate answer to these questions may be ob- 
tained from the data of Table I. In column II of 
that Table are recorded the average wages of unskilled 
laborers in the several dejKirtements. In column V, the 
local values are tabulated of our representative of the 
standard of life — the prix ordinaire de ])ensio7i paye 
par Vouvrier isole pour le logement et la nourriture. 

From these data we find — 

(1) that the money wages of unskilled laborers vary 

in the same direction as the cost of the stand- 
ard of life ; 

(2) that the law of the association of the money 

wages of unskilled laborers and the cost of the 
standard of life is linear ; 

(3) that the money wages of unskilled laborers are 

much more closely related to the cost of the 
standard of life than to the cost of the means 
of subsistence. In the former case r=. 667; 
in the latter, r= .306. 

The graph representing the relation of the two 
variables is given in Figure 3. In making the com- 
putations, all of the departements for which records ex- 
ist were considered except Gironde and Maine-et- 
Lolre. 

Figure 3 exhibits the law of the variation of wages 



Means of Subsistence and the Standard of Life 35 







36 Laws of Wages 

of unskilled laborers as the prix de pension varies from 
departement to departement. If the prix de p)ension 
were taken as a function of the wages of unskilled 
laborers we should have, as the equation of the rela- 
tion between the two variables, ?/=.5786 a; +.2537, 
where x is put for the wages of unskilled laborers. 
From this equation it is clear that, for an increase 
of one franc in the wages of unskilled laborers, 
there is on the average an increase of about 58 
centimes in the p)rix de pension. 

There is a subtle difficulty to be overcome before 
our investigation can be brought into closer relation 
with the Ricardian doctrine. The preceding results 
are conclusions as to the relation between money 
wages and the prix de pension. But the Ricardian 
doctrine, postulating an invariable money unit, is a 
theory as to the relation of wages and the concrete 
things composing the standard of life. Would it be 
possible to close the gap between our results and the 
Ricardian theory ? 

The statistical calculus supplies the tool for connect- 
ing the empirical conclusions with the a priori doctrine. 
Thus far it has been shown that the money wages of 
unskilled laborers are correlated with the p)rix de 
p>ension and also with the coefficient de depense en oh- 
jets d' alimentation et de chauffage. Let us represent 
the coefficient measuring the correlation in the first 
case by rjo, and in the second case by r^^. The coeffi- 
cient de depense, we know, is the money value of the 
same kinds and quantities of things in the different de- 



Means of Subsistence and the Standard of Life 37 

partements, while the prix de pension is the price of 
a standard that varies from departement to departement. 
As the former represents the variation in the purchas- 
ing power of money in the different regions of France, 
we should infer that the prix de pension would be 
correlated with the coefficient de depense. Let the 
measure of correlation in this case be r.^^. In order 
to connect our results with the Ricardian theory it is 
necessary to eliminate from the empirical conclusion 
as to the relation of the money wages of unskilled 
laborers to the price of the standard of life the factor 
due to the local variation in the purchasing power of 
money. 

According to the theory of the partial coefficient 
of correlation/ if three variables are so interrelated 
that their gross coefficients of association are respec- 
tively ri2, ^13, ^237 then the partial or net coefficient of 
correlation between the variables 1 and 2 is measured 

by /)i2 = ^^ ^^ ^'^ Using this method of 

Vl - 7*13^ Vl - nj 

treating our problem, we find that the net correla- 
tion between the wages of unskilled laborers and 
their standard of life is pi2 = -628, where the r sym- 
bols in the above formula for ^^2 have the meanings 
described in the preceding paragraph. The actual 
values of these coefficients are ri2= .6667 (the coeffi- 
cient of correlation between money wages of un- 
skilled laborers and the prix de pension) ; r^g = .3064 

^ See G. Udny Yule : " On The Theory of Correlation." Journal 
of the Royal Statistical Society, December, 1897. 



38 Laws of Wages 

(the coefficient of correlation between the money 
wages of unskilled laborers and the coefficient de 
depense en ohjets d' alimentation et de chauff'age) ; 
7'23=.3405 (the coefficient of correlation between the 
prix de pension and the coefficient de depense en ohjets 
d' alimentation et de cliaujfage)} 

From this result it follows that, so far as the data 
upon which the investigation rests may be assumed 
to be representative of the true values of the factors 
in the problem, the degree of association between the 
wages of unskilled laborers and their standard of 
life ^ is measured by pi2 = .628. 

1 In computing the value of rgg, all of the records were used ex- 
cept that for Lozere. 

2 I have been unable to find in the French report any precise def- 
inition of the term I'ouvrier isole as it appears in the investigation 
concerning /)nx de pension pai/e par Vouvrier isole j^our le logement et la 
nourriture. Does it refer to the single unskilled laborer, or to the 
single skilled laborer, or was it impossible to measure the difference 
between the prix de pension of the two classes of laborers? The last 
interpretation would seejii most probable; for the attempt, in Vol. IV, 
p. 260, to compare the wages of skilled and of unskilled laborers with 
the prix de pension pniji par I'ouvrier isole assumes a common prix de 
pension for the two classes of laborers. 

It may be noted incidentally that the present chapter contains a 
solution of the problem that is abandoned in the French report. 
" A vrai dire, la relation qui pent exister entre le salaire et la depense 
pour le logement et la nourriture ne semhle ni directe, 7ii simple." — p. 260. 
The relation is both direct and simple and the coefficient measuring 
the degree of the net relation is p = .628. 

The justness of taking the prix de pension as the representative of 
the standard of life of unskilled laborers is reenforced by the consid- 
eration that the mean value of t\\e prix de pension d'lm ouvrier isole is 
76 per cent of the mean value of the wages of unskilled laborers. 
It therefore represents with a high degree of accuracy the effort of 
the unskilled laborer to maintain a standard that varies from 
de'partement to departement. 



Means of Subsistence and the Standard of Life 39 

' Wages of Skilled and of Unskilled Laborers. 

Table I supplies data for measuring a relation that 
has great importance for the theory of Chapter IV, 
and for the appreciation of practical schemes that 
have for their aim the raising of the level of general 
wages. What is the relation between the variation 
in the wages of skilled and of unskilled laborers ? 
The results that are about to be given are based 
upon a consideration of all of the 87 departements 
of France, except three, — Seine, Seine- et-Marne, 
Seine-et-Oise, which are unduly affected by the pecul- 
iar conditions of wage receiving in Paris. 

We find — 

(1) that the wages of skilled and of unskilled la- 

borers vary in the same direction ; 

(2) that the law of the relation is linear ; 

(3) that the coefficient of correlation is r = .775, 

which is hio;her than the coefficient measur- 
ing the correlation between the wages of 
unskilled laborers and the cost of the stand- 
ard of life. 

The graph representing the relation is given in 
the accompanying Figure 4. The equation to the 
straight line is ?/ = 1.24 + .9142 x, where x = the wages 
of unskilled laborers. 

Inasmuch as both classes of wages are affected 
by the local variations in the purchasing power of 
money, the net relation between the two variables 



40 



Laws of Wages 



































































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Means of Subsistence and the Standard of Life 41 

can be found only after the money factor is elimi- 
nated. If, as in a previous case, we represent the 
correlation between the wages of skilled laborers and 
the wages of unskilled laborers by r^g ; the correla- 
tion between the wages of skilled laborers and the 
coefficient de depense en ohjets d' alimentation et de 
chauffage by i\2, 5 ^^^^ "t^^^ correlation between the 
wages of unskilled laborers and the coefficient de de- 
pense by r2z', then, the net correlation between the 
wages of skilled laborers and the wages of unskilled 

laborers is /)i2= •'''S^- 

We have now definite quantitative solutions to the 
problems we set out to examine. The wages of un- 
skilled laborers vary, from place to place in the same 
country, directly (1) with the cost of the means of 
subsistence, (2) with the standard of life, the close- 
ness of the relation being measured, respectively, 
by r=.306, /)=.628. The wages of skilled laborers 
vary directly with the wages of unskilled laborers, 
the degree of the association being measured by 
/) = .757. 

The very high correlation between the wages of 
skilled laborers and the wages of unskilled laborers 
suggests the wisdom of further investigation as to 
the mechanism of their relation. This investigation 
is supplied in Chapter IV, on " Wages and Ability." 



42 



Laws of Wages 






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Means of Subsistence and the Standard of Life 43 



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CHAPTER III 

WAGES AND THE PRODUCTIVITY OF LABOR 

" However wages may be adjusted by bargains freely made by 
individual men, the rates of pay that result from such transactions 
tend ... to equal that part of the product of industry which is 
traceable to the labor itself." 

" We must ascertain whether evolution makes labor more pro- 
ductive, and therefore better paid, or less productive and therefore 

worse paid." 

— John Bates Clark. 

A COMPLETE theory of wages faces two fundamental 
inquiries: (1) as to the law and cause of the varia- 
tion in the share of the product of industry consti- 
tuting general wages ; and (2) as to the law and 
cause of the distribution of general wages among the 
members of the labor group. According to the pro- 
ductivity theory of wages, the principle of the specific 
productivity of labor supplies the clew to the satis- 
factory solution of both inquiries. It is the purpose 
of the present chapter to treat statistically certain 
phases of the first part of this theory, which is con- 
cerned with the determination of the rate of general 
wages. In the following chapter the second part 
will receive its proper attention. 

We shall approach the very kernel of the produc- 
tivity theory by successive stages. Three essential 
propositions in the theory will be established. It 

44 



Wages and the Productivity of Labor 45 

will be demonstrated first that in a particular indus- 
try in which labor plays a relatively large role in 
production, the fluctuation in the rate of general 
wages varies directly with the fluctuation in the 
value of the product per laborer. It will then be 
established that the fluctuation in the laborer's rela- 
tive share in the value of the product varies directly 
with the fluctuation in the amount of machine-power 
per laborer employed in the industry. In the third 
place, a proof in a particular instance will be supplied 
of an important dynamic corollary of the productivity 
theory of wages, namely, that, other conditions re- 
maining the same, the general trend of the laborer's 
share of the product is determined by the ratio in 
which capital and labor are combined in production. 
These three investigations will bring to a statistical, 
test the essential propositions in the productivity 
theory : the rate of general wages will be related 
to the productivity of labor, and the secular trend 
of the laborer's share in distribution will be brought 
into functional dependence upon the ratios in which 
capital and labor cooperate in production. 

Descrijjtion of Data. 

The data forming the basis of the investigation 
are drawn from the history of coal mining in France. 
It is highly desirable that all three of the proposi- 
tions which have just been described should be in- 
vestigated with reference to the same industry, and 
it is necessary, if the statistical inductions are to 



46 Laws of Wages 

have value, that the investigation should extend over 
a great number of years. These desiderata obviously 
impose unusual statistical conditions in the selection 
of material ; for they require that the statistical 
record shall cover many items that are difficult to 
ascertain and shall, in addition, be relatively uniform 
over a long period in its method of tabulation. 
There is only one ^ industry in France for which the 
required material is supplied, and I am not aware of 
the existence in any other country of data comparable 
in fullness of detail and in length of time over which 
the record is available. The figures upon which the 
investigation rests, and which appear in the three 
tables at the end of this chapter, have been taken 
from the careful work by M. Francois Simiand^ on 
Le Salaire des ouvriers des mines de charhon en France. 

Fluctuations in the Rate of Wages and in the Value 
of the Product. 

The first proposition to be established is that, in 
an industry in which labor plays the leading role in 
production, the fluctuation in the daily rate of gen- 

1 " La seule Industrie dont en France on connaisse chaque ann6e 
par une publication officielle le nombre des ouvriers, leur salaire 
nioyen journalier et leur gain annuel, la production et le prix de 
vente, est celle des mines de houille." — Levasseur : Salariat et Salaires, 
p. 31. 

^ M. Simiand has dealt in his own manner with the first proposi- 
tion developed in this chapter. His acute study also contains a 
valuable section on the relation of the use of machinery to the rate 
of wages. I am greatly indebted to M. Simiand for the data that I 
have taken from his masterly treatise, but I have not borrowed froin 
him either method or ideas. 



Wages and the Productivity of Labor 47 

eral wages varies directly with, the fluctuation in the 
value of the daily product per laborer. The proposi- 
tion is taken in this form simply as a first approxi- 
mation to the theoretical principle that the rate of 
wages varies directly with the marginal productivity 
of labor. 

It is quite a difficult task to ascertain directly the 
statistical equivalent of the marginal productivity of 
labor, and, of course, no record exists of the varia- 
tion of the marginal productivity throughout a term 
of years. Fortunately for the inductive proof of 
this important principle, it is not necessary to treat 
the theory in the form of the marginal statement. The 
way out of the difficulty has been supplied by the 
analysis of Professor Clark. 

In its cruder form, as it was first enunciated in 
principle by Von Thiinen, the marginal^ productivity 
theory of wages implied that at a given time the 
marginal laborer — who for the sake of simplicity 
was assumed to be the laborer most recently set at 
work — produced less than the laborers who w^ere 
employed earlier, and that the advent of the mar- 
ginal man not only reduced the amount that could be 
claimed by all the laborers, but was the occasion for 
diverting a part of the product of the earlier laborers 
to capitalists and entrepreneurs. It was one of the 
many services of Professor Clark to show that the spe- 
cific product of every unit of labor is equal to the 

^rt is not meant to suggest that Von Thiinen used the words 
** marginal productivity." 



48 Laws of Wages 

product of the marginal unit, that, at any given time, 
all units are alike in their productivity, that the fall 
in the productivity of labor occasioned by the advent 
of a new worker is due to a reapportionment of capi- 
tal which gives to each laborer a smaller amount of 
capital as cooperating adjunct, and that the produc- 
tivity of general labor is equal to the sum of the pro- 
ductivity of its constituent items. In view of this 
analysis, it follows that if an industry could be dis- 
covered in which labor played the chief role in pro- 
duction, the variations in the mean value of the 
product per laborer per day would be a close first 
approximation to the variations in the specific pro- 
ductivity of labor. 

Table I, in the Appendix to this chapter, has been 
compiled as follows : Column II, giving the mean 
daily rate of wages, is derived from two items, (1) 
the total amount paid annually in wages, and (2) 
the number of days' work during the year. This 
second item is equal to the sum of the products of 
the number of laborers employed for various intervals 
of the year by the number of days during which they 
were respectively employed. Item (I) divided by 
item (2) gives the mean daily rate of wages tabu- 
lated in column 11.^ Column III is likewise derived 
from two items, (1) the value of the total annual prod- 
uct at the place of production, (2) the number of 
days' work during the year. The second item is the 

1 Simiand : Le Salaire des ouvriers des mines de charbon en France, 
pp. 24-25. 



Wages and the Productivity of Labor 49 

same as the second item in the preceding case. The 
figures tabulated in column III, giving the mean 
value of the daily product per laborer, are the ratios, 
for successive years, of the value of the annual prod- 
uct divided by the aggregate number of days' work 
per year.^ Columns II and III, which record the 
simultaneous variations of the two factors for a 
period of fifty-six years, afford an ample basis for 
investigating the relation between the mean daily rate 
of wages and the mean value of the daily product per 
laborer. It should be remembered that, in case of the 
French coal miners, no formal sliding scale system 
by which wages varied with the value of the product 
existed during the period covered by this study .^ 

On Figure 5 is traced, for a period of fifty-six years, 
the history of the variation of the mean daily wages 
and of the mean value of the daily product per 
laborer. In each case the history of the change is 
recorded in an ascending zigzag line, which is the re- 
sultant of the forces determining its mean direction 
and the forces producing the vicissitudes portrayed in 
the fluctuations about the line of general trend. The 
proposition with which we are at present concerned is 
that, at a given time, the variation in the productiv- 

^ Simiand : Le Salaire des ouvriers des mines de charbon en France, 
p. 98. 

2 " Sans doute, nous savons qu'en fait le systeme dit de Vechelle mo- 
bile, qui fait varier le salaire suivant une certaine relation, en raison 
des variations du prix du produit dans le sens de la baisse aussi bien 
que dans le sens de la hausse, n'a jamais 6t6 adopts par les ouvriers et 
patrons franc^ais." — Simiand: Le Salaire, etc., p. 227. Cf. also pp. 
195-196, 196 n. 



50 



Laws of Wages 



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Wages and the Productivity of Labor 51 

ity of labor is accompanied with a variation of wages 
in the same direction. That is to say, as an average 
result, an increase or decrease in the productivity of 
labor is accompanied with an increase or decrease in 
wages. This proposition, therefore, is a thesis affect- 
ing the fluctuations about the general trend, and con- 
sequently, in order to bring the two series to a 
comparable basis, their differences due to their differ- 
ence in general trend must be eliminated. Our first 
problem, then, is to find the equation to the general 
trend of the figures in each series. 

If the type of equation for each series be taken as 
of the geometric order y = AB^, and the constants 
A, B be evaluated by the method of moments, the 
equation to the general trend for the wage series is 
y= 2.1063(1.015)% and, for the series of the values of 
the product, ?/ = 5.1115(1.012)% the origin, in both 
cases, being at 1847. The two equations are repre- 
sented upon Figure 5 by the smooth curves passing 
through the two series of numbers. 

The knowledge of the equations to the curves of 
general trend makes possible the next step in the 
problem, which is the computation of the relative 
deviations of the actual figures from the general trend. 
The actual figures, as we know, are recorded by the 
zigzag line. The absolute deviations of the actual 
figures for the successive years are obtained by sub- 
tracting from the actual figure for each year the 
value of the general trend for the same date. For 
example, the absolute deviation for 1900, in case of 



52 



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Wages and the Productivity of Labor 53 

the daily product, was 10.78 — 9.43 = 1.35, because 
the mean value of the daily product per laborer, in 
1900, was 10.78 francs, and the value of the general 
trend for the same year was 2/= 5.1115 (1.012)^' = 
9.43 francs. The relative deviation of the actual 
figures for each year is the ratio of the absolute devi- 
ation to the corresponding value of the general trend. 

1 35 

In 1900, the relative deviation was — — = 14.3 per 

9.43 ^ 

cent. It is desirable to deal with the relative, in- 
stead of the absolute, deviations because the two 
series of figures move about axes with different 
absolute values and with different rates of change. 

After the relative deviations of the two series of 
figures have been computed, it is possible to treat 
their correlation. On Fiarure 6 the relative devia- 
tions of the two series are plotted about a horizontal 
line. It is quite evident from the general concurrent 
flow of the curves that the two series of percentage 
deviations are closely associated. What is the meas- 
ure of the degree of their correlation ? 

The computation of the coefficient of correlation 
by the usual method gives r = .843. Figure 7 
shows the regression of the percentage deviation 
in the mean daily wage upon the percentage devi- 
ation in the mean value of the daily product per 
laborer. 

We conclude, therefore, from this part of the in- 
vestigation, that, in case of the great industry of coal 
mining in France, — 



54 



Laws of Wages 









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Wages and the Productivity of Labor 55 

(1) the fluctuation in the mean daily rate of wages 

varies directly with the fluctuation in the 
mean value of the daily product of the 
laborer ; 

(2) the coefhcient measuring the degree of associa- 

tion between the percentage variation in the 
rate of wages and the percentage variation in 
the mean value of the daily product per laborer 
has the very high value of r = .843. 

Fluctuations in the Laborer's Relative Share of the 
Product and in the Ratio of Capital to Labor. 

The second essential proposition in the productivity 
theory of wages is that the fluctuation in the laborer's 
relative share in the value of the product varies di- 
rectly with the fluctuation in the amount of machine 
power per laborer employed in the industry. The 
establishment of this proposition in a rigid form 
would give to the productivity theory in its most 
important aspect the sanction of inductive proof. 
For the pure theory of the distribution of income is 
a theory as to the apportionment of the product of 
industry between the agents cooperating in its pro- 
duction and is, therefore, concerned with relative 
shares of the product and not with their absolute 
magnitudes. Our first proposition concerning the 
relation of wages to the value of the product is a 
proposition affecting the absolute value of wages and 
not the laborer's relative share of the product of in- 
dustry. The proposition that we are about to ex- 



56 Laws of Wages 

amine is concerned with the latter, more fundamental 
aspect of the wages question. 

Table II in the Appendix exhibits the material 
upon which the investigation rests. Column II of 
that table gives, throughout a period of 53 years, the 
ratio of a day's wages to the value of a day's product 
per laborer. The two items from which the ratios 
are derived may be obtained from Table I. Column 
III, which gives the amount of machine-power per 
100 laborers employed in mining, is derived from two 
items that are taken from M. Simiand's work ^ : 
(1) the total horse-power of the machinery employed 
in the mines, and (2) the number of laborers so em- 
ployed. The figures in column III are the ratios of 
these two items expressed as the number of horse- 
power per 100 laborers. The problem that will 
be investigated is tlie relation of the variations 
of the figures in column II to the variations in 
column III. 

It would have been desirable to investigate directly 
the relation of the variation of the laborer's share of 
the product to the variation of the amount of capital 
associated with labor in production. But the figures 
for the capital employed, at successive years, were 
not accessible to me. The proposition in the form in 
which it will be tested is of first importance in itself, 
and if it is permitted to make the reasonable assumption 
that the machine-power employed in mines is directly 
related to the amount of capital employed, then the 

1 Simiand : Le Salaire, p. 49. 



Wages and the Productivity of Labor 57 

establishment of the proposition in its present form 
renders practically certain the doctrine of pure eco- 
nomics that the laborer's relative share of the product 
varies directly with the relative amount of capital 
with which he works. 

A moment ago reference was made to the exploita- 
tive implication in Von Thiinen's treatment of the 
productivity principle. To affirm that the marginal 
product of labor decreases with an increase in the 
labor force and that the general rate of wages falls 
with the decrease of the marginal product, leaves 
room for the inference that the earlier laborers are 
exploited of a part of their product when, in conse- 
quence of the growth of the labor force, the marginal 
product of labor decreases. Professor Clark, as we 
know, has shown why such an inference is unwar- 
ranted. The explanatory facts are that the increase 
of the labor force implies a reduction in the average 
amount of capital with which the laborer works, and 
that the fall of the general rate of wages is due to a 
lessened specific productivity of labor following the 
per capita reduction of the amount of capital employed. 
Has this theory relevancy only to the hypothetical 
static state that forms the groundwork of theoretical 
speculation, or does it have a bearing upon the highly 
dynamic conditions of actual industry ? The investi- 
gation that we are about to enter upon will answer 
the question. 

Our present query has this form : Does the fluctua- 
tion in the laborer's relative share of the product of 



58 



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Wages and the Productivity of Labor 59 

industry vary directly with the fluctuation in the 
relative amount of machine-power with which he 
works, and if so, how closely are the concomitant 
variations related ? 

The method of investigation is the same as the one 
we have already employed. If the quantities in col- 
umns II and III of Table II are plotted, the graphs will 
take a generally ascending zigzag course. The equa- 
tion to the general trend, in case of the ratio of wages 
to the value of the product, is ?/ = 40.756(1.0039f, 
and, in case of the ratio of machine-power to men, 
2/ = 28.758(1.025)% the origin in both cases being 
1847. On Figure 8 the percentage deviations are 
traced about a horizontal line, and on Figure 9 the 
regression of the percentage deviation of the first 
series upon the percentage deviation of the second 
series is shown, that is to say, the regression of the 
percentage deviations, in case of the ratio of wages 
to the value of the product, upon the percentage 
deviations in case of the ratio of machine-power to 
men. The coefficient of correlation is r = .599. 

We conclude, so far as the industry of coal mining 
in France is concerned, — 

(1) that the fluctuation in the laborer's relative 

share of the product of industry varies directly 
with the fluctuation in the relative amount 
of machine-power with which he works ; 

(2) that the coefficient of correlation is /■= .599. 

(3) that if it is permitted to assume that the 



60 



Laws of Wages 




^ d 
>>3 



»- fl 



♦ ♦l-l-H- lllllll 



Wages and the Productivity of Labor 61 

amount of machine-power varies directly with 
the amount of capital employed, then the 
fluctuation in the laborer's relative share of 
the product of industry varies directly with 
the fluctuation in the relative amount of 
capital employed. 

17ie General Trend of Wages. 

The third essential proposition in the productivity 
theory of wages is that, other conditions remaining 
the same, the general trend of the laborer's relative 
share of the product is dependent upon the ratio in 
which capital and labor are combined in production. 
Up to this point we have been concerned with fluctua- 
tions about the general trend of wages ; we now enter 
upon the question of the general trend itself. This 
corollary of the productivity theory is a proposition 
in dynamic economics ; it concerns the reward of the 
laborer in a society in which conditions and methods 
of production are changing, and consequently it has 
a very direct bearing upon concrete industry. 

Because of the lack of data to treat this proposition 
fully, we shall be compelled to approach the problem 
by investigating, in a particular instance, a corollary 
of the proposition before us. We observe, then, that 
if it be true that the general trend of the laborer's 
relative share of the product of industry increases 
with the relative amount of capital with which he 
works, it would follow that, in the same industry, in 



62 LaiDs of Wages 

neighboring places, with similar methods of produc- 
tion, the general trend of the laborer's share would 
increase most rapidly where the general trend of the 
relative amount of capital per laborer employed in- 
creased most rapidly. Or, to put the corollary in a 
form in which it Avill admit of treatment by means 
of available statistics, we may say that in case of 
the same industry, in neighboring places, other con- 
ditions remaining the same, the general trend of the 
laborer's relative share of the product will increase 
most rapidly where the general trend of machine 
power per laborer increases most rapidly. 

Table III in the Appendix exhibits the data used 
in the investigation. Column II gives the ratio, per 
hundred laborers, of the machine-power employed in 
the direct exploitation of the coal mines in the Bassin 
de Nord. Column III gives, for the same basin and 
the same period, the ratio of daily wages per laborer 
to the value of the daily product per laborer. Columns 
IV and V give the corresponding data for the neigh- 
boring Bassin de Pas-de-Ccdais. All of the figures 
have been taken from M. Simiand's work.^ The 
record for the period 1880-1902 is used because the 
figures for the years before 1880 are not comparable 
with those for the later period. M. Simiand gives 
figures for only three basins — Loire, Nord, and Pas- 
de-Calais. The methods of exploitation and the gen- 
eral conditions of production in case of the neighboring 
basins Nord and Pas-de-Calais are regarded by M. 

1 Simiand: Le Salaire, p. 112. 



Wages and the Productivity of Labor 63 

Simiand as being so much alike as to justify his class- 
ing them together ^ and treating them in sharp con- 
trast to the southerly Bassin de Loire. 

It is quite clear, therefore, that the Bassin de Nord, 
and the Bassin de Pas-de- Calais, because of their be- 
ing in neighboring departements, because of the simi- 
lar methods of exploitation and the similar general 
conditions of production, and because of the exist- 
ence of statistical material covering a long period, 
offer a favorable case for testing the corollary that 
has just been formulated. 

Our immediate problem is to find, for the two coal 
basins, the general trend of the increase, first of the 
ratio of the machine-power per hundred laborers, and 
secondly, of the ratio of wages to the value of the 
product. In case of the data as to the ratio of 
machine-power to the number of men, we find, by us- 
ing the same method that has already been employed 
in this chapter, that the equation to the general trend 
for the Bassin de Word is ?/ = 46.815(1.0504)-«, and 
for the Bassin de Fas-de- Calais, 7/ = 61.793(1.0344)% 
the origin in both cases being at 1880. As both of 

1 Simiand: Le Salaire, pp. 110-111. "II suffit a uotre dessein de 
consid6rer les bassins dont Timportance domine et regie revolution 
globale et d'atteindre les cas d'6volutioii 6conomique les plus diver- 
gents que nous puissious rencontrer. Or, il se trouve qu'a tons les 
moments de notre experience, Loire, Nord et Pas-de-Calais fournissent 
a eux seuls la plus grosse part de la production franpaise totale (d'abord 
sensiblement plus de la moiti^, ensuite jusqu'a 70% et plus). Puis une 
etude anterieure nous a indiqu6 que le bassin de la Loire d'une part, 
les bassins du Nord et du Pas-de-Calais de I'autre, semblaient s'opposer 
le plus nettement au point de vue de la conduite 6conomique." 



64 



Lairs of Wages 










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Wages and the Productivity of Labor 65 

these equations are of the geometric form, it follows 
that the ratio of annual increase in the ratio of 
machine-power per hundred men, for the Bassin de 
Nord is 1.0504, and for the Bassin de Pas-de-Calais 
is 1.0344. Hence, as the Bassin de Nord offers the 
greater ratio of increase, we should expect to find, 
according to the principle of the productivity theory, 
that the ratio of the laborer's relative share in the 
product increased more rapidly in the Bassin de Nord 
than in the Bassin de Pas-de- Calais. Before passing 
to the question of wages, we should note that, if the 
equations to the general trend for the relative machine 
power in the two cases be put in the form, respec- 
tively, of 2/= 100(1.0504)% and ?/= 100(1.0344)% the 
upper part of Figure 10 will represent the relative 
ratios of increase for the two basins. 

In case of the data as to the ratio of wages to the 
value of the product, we find that the equation to 
the general trend for the Bassin de Nord is 
2/ = 49.139(1.0035)% and for the Bassin de Pas-de- 
Calais, 2/ = 44.697 (1.0013)% the origin in both cases 
being at 1880. The ratio of the annual increase in 
the former case is 1.0035 and in the latter case it is 
1.0013. If the two equations be put in the form of 
?/= 100 (1.0035)" and ?/ = 100 (1.0013)% respectively, 
the lower part of Figure 10 will represent, for the two 
basins, the ratios of increase of the laborer's relative 
share of the product. i 

1 In order to make visible the ratios of growth in the two cases, the 
upper and the lower parts of Figure 10 are drawn to different perpen- 
dicular scales. 



66 Laws of Wages 

We find, accordingly, that, true to the principle of 
the productivity theory, — 

(1) the general trend of the laborer's share of the 

product is upward where the general trend of 
machine-power per laborer is upward ; 

(2) the ratio of increase in the general trend of 

wages is greater, the greater the ratio of in- 
crease in the relative amount of machine- 
power with which the laborer works. 

If it is reasonable to assume that the amount of 
machine-power employed in coal mining varies directly 
with the amount of capital employed, the preceding 
investigation justifies the conclusion that the increase 
in the general trend of the laborer's share of the prod- 
uct is greater, the greater the increase in the general 
trend of the ratio of capital to labor employed in pro- 
duction. 

The conclusions of this chapter have, for the most 
part, been expressed in general form, while the ma- 
terial upon which the investigation rests has been 
drawn from the history of one industry in one country. 
This has been done with no intention of exaggerating 
the scope of the inductive inferences nor in ignorance 
of the narrow statistical basis upon which the last 
proposition rests. The purpose of the investigation 
was to make the connection between certain general 
conclusions of pure economics and the concrete facts 
of some one great industry. The general character of 



Wages and the Productivity of Labor 67 

the propositions is due to their a priori origin ; the 
investigation has established that, far from being 
without relevancy to actual industry, these general 
propositions are the accurate description of the eco- 
nomic laws of wages in the one great industry that 
has been subjected to inductive treatment. 



68 



Laws of Wages 



APPENDIX 

TABLE I. — Daily Wages and Mean Value of Daily Product 
PER Laborer 







Mean Value 






Mean Value 


Year 


Mean Daily 
Wages 


of the 
Daily Product 
per Laborer 


Year 


Mean Daily 
Wages 


of the 

Daily Product 

per Laborer 


I 


II 


III 


I 


II 


III 


1847 


2.07 


5.13 


1875 


3.58 


8.41 


1848 


2.14 


4.76 


1870 






1849 


2.16 


5.09 


1877 






1850 


2.14 


5.27 


1878 







1851 


2.07 


4.75 


1879 






1852 


2.04 


4.81 


1880 






1853 


2.20 


5.32 


1881 







1854 


2.32 


5.40 


1882 


3.71 


7.91 


1855 


2.35 


5.95 


1883 


3.84 


8.06 


• 1856 


2.51 


6.32 


1884 


3.83 


8.06 


1857 


2.48 


5.93 


1885 


3.72 


8.05 


1858 


2.55 


5.97 


1886 


3.71 


7.71 


1859 






1887 


3.72 


7.65 


1860 


2.50 


5.73 


1888 


3.71 


7.60 


1861 


2.57 


5.94 


1889 


3.87 


7.88 


1862 


2.52 


5.89 


1890 


4.16 


8.84 


1863 


2.69 


5.83 


1891 


4.17 


9.09 


1864 


2.60 


5.69 


1892 


4.24 


8.46 


1865 


2.69 


6.02 


1893 


4.14 


8.03 


1866 


2.76 


6.31 


1894 


4.14 


8.01 


1867 


2.89 


6.52 


1895 


4.10 


7.93 


1868 


2.96 


6.45 


1896 


4.10 


7.86 


1869 


2.99 


6.58 


1897 


4.14 


8.08 


1870 


3.04 


6.55 


1898 


4.23 


8.41 


1871 


3.08 


6.88 


1899 


4.38 


9.21 


1872 


3.35 


7.91 


1900 


4.66 


10.78 


1873 


3.45 


9.30 


1901 


4.82 


10.68 


1874 


3.56 


8.93 


1902 


4.57 


9.75 



Wages and the Productivity of Labor 



69 



TABLE II. — Ratio of Daily Wages to the Value of a Day's 
Product per Laborer and Ratio of Machine-Power to 
One Hundred Laborers 





Katio of 






Ratio of 






Daily Wages 


Eatio of 




Daily Wages 


Ratio of 


Tear 


to the Value 


Machine-Power 


Year 


to the Value 


Machine-Power 


of a Day's 


to 100 




of a Day's 


to 100 




Product per 


Laborers 




Product per 


Laborers 




Laborer 






Laborer 




I 


II 


III 


I 


II 


III 


1847 


40.4 


32 


1874 


39.9 


43 


1848 


45.0 


37 


1875 


42.6 


45 


1849 


42.5 


36 


1876 


43.1 


51 


1850 


40.7 


34 


1877 


45.0 


54 


1851 


43.6 


36 


1878 


45.5 


59 


1852 


42.5 


36 


1879 


45.7 


61 


1853 


41.4 


32 


1880 


45.2 


64 


1854 


43.0 


34 


1881 


45.6 


65 


1855 


39.5 


34 


1882 


46.9 


68 


1856 


39.7 


36 


1883 


47.7 


67 


1857 


41.8 


39 


1884 


47.5 


72 


1858 


42.7 


44 


1885 


46.2 


77 


1859 




— 


1886 


48.1 


82 


1860 


43.7 


44 


1887 


48.6 


81 


1861 


43.3 


42 


1888 


48.8 


82 


1862 


42.8 


. 41 


1889 


49.1 


79 


1863 


46.2 


39 


1890 


47.0 


85 


1864 


45.7 


38 


1891 


45.8 


87 


1865 


44.7 


40 


1892 


50.2 


92 


1866 


43.8 


44 


1893 


51.7 


100 


1867 


44.3 


44 


1894 


51.7 


108 


1868 


45.9 


45 


1895 


51.7 


105 


1869 


45.5 


47 


1896 


52.1 


108 


1870 


46.4 


49 


1897 


51.3 


111 


1871 


44.8 


48 


1898 


50.3 


111 


1872 


42.3 


44 


1899 


47.6 


110 


1873 


37.1 


41 









70 



Laws of Wages 



TABLE III. — Ratio of Machine-Power to One Hundred 
Laborers and Ratio of Daily Wages to the Value of a 
Day's Product per Laborer 





Bassi> 


DE NORD 


BaSSIN DE 


Pas-de-Calais 


Tear 


Ratio of 

Machine-Power 

to 

100 Laborers 


Ratio of Daily 

Wages to tlie 

Value of a Day's 

Product per Laborer 


Ratio of 

Machine-Power 

to 

100 Laborers 


Ratio of Daily 

Wages to the 

Value of a Day's 

Product per Laborer 


I 


II 


III 


IV 


V 


1880 


45 


48.7 


64 


40.2 


1881 


46 


49.3 


63 


42.3 


1882 


48 


49.0 


71 


45.0 


1883 


50 


49.9 


72 


45.2 


1884 


58 


51.5 


70 


45.7 


1885 


68 


50.1 


70 


44.1 


1886 


69 


50.6 


85 


45.8 


1887 


71 


49.9 


82 


46.6 


1888 


77 


49.9 


83 


46.5 


1889 


77 


48.8 


79 


47.4 


1890 


82 


47.4 


75 


44.3 


1891 


79 


45.5 


78 


40.9 


1892 


85 


50.0 


83 


47.5 


1893 


90 


54.8 


94 


49.5 


1894 


91 


56.7 


115 


48.4 


1895 


90 


57.9 


104 


49.0 


1896 


95 


56.8 


101 


49.8 


1897 


93 


55.3 


110 


49.2 


1898 


92 


53.7 


109 


49.0 


1899 


107 


51.6 


97 


44.5 


1900 


137 


45.8 


125 


39.8 


1901 


153 


50.5 


149 


42.2 


1902 


156 


52.7 


146 


42.1 



CHAPTER IV 

WAGES AND ABILITY 

" Le capitalisme . . . tend a produire vine certaine ^galisation du 
travail entre les diverses parties de I'usine ; mais comme il a besoin 
d'un nombre considerable d'hommes particulierement actifs, attentifs 
ou experiment's, il s'ing6nie a donner des supplements de salaire aux 
hommes qui lui rendent ainsi plus de services ; ce n'est point par 
des considerations de justice qu'il se regie dans ce calcul, mais par 
la seule recherche empirique d'un equilibre r^gie par les prix. Le 
capitalisme arrive done a r'soudre un probleme qui semblait insolu- 
ble, tant qu'il avait 6t6 etudie par les utopistes ; il r'sout la ques- 
tion de regalite des travailleurs, tout en tenant compte des inegalites 
naturelles ou acquises qui se traduisent par des inegalites dans le 
travail." 

— Georges Sorel. 

In the preceding chapter we examined statistically 
the most important aspects of the first of the two in- 
quiries that are faced in a complete theory of wages, 
namely, the question as to the law and cause of the 
variation in the share of the product of industry con- 
stituting general wages. In the present chapter we 
shall be concerned with the second of these funda- 
mental inquiries, namely, with the law and cause of 
the distribution of general wages among the members 
of the labor group. Our point of departure is Pro- 
fessor Marshall's treatment of the topic. 

" We may then regard competition, or, to speak 
more exactly, economic freedom and enterprise, as 
tending to make time-earnings in occupations of 

71 



72 Laws of Wages 

equal difficulty and in neighbouring places not equal, 
but proportionate to the efficiency of the workers." ^ 
The sense in which Professor Marshall uses the word 
" efficiency " is to be inferred from the context. He 
defines " efficiency-ivages " as " earnings measured, 
not as time-earnings are with reference to the time 
spent in earning them ; and not as piece-work earn- 
ings are with reference to the amount of output re- 
sulting from the work by which they are earned ; 
but with reference to the exertion of ability and effi- 
ciency required of the worker." ^ In the fourth book 
of the Principles of Economics, Chapter V opens with 
this sentence : " We have next to consider the con- 
ditions on which depend health and strength, physical, 
mental and moral. They are the basis of industrial 
efficiency, on which the production of material wealth 
depends." Elsewhere,^ Professor Marshall asserts 
" that what makes one occupation higher than an- 
other, what makes the workers of one town or coun- 
try more efficient than those of another, is chiefly a 
superiority in general sagacity and energy which is 
not specialized to any one trade." From these refer- 
ences it may be inferred that the term " efficiency " 
when applied in the theory of wages in a subjective 
sense ^ means a balance of physical, mental, and moral 

1 Principles of Economics. 4th edit., p. 6-30. 

^Ibid., pp. 630-631. ^ Ibid., p. 286. 

*The word "efficiency" is one of a large group of terms — such 
as belief, truth, probability — in which there is ambiguity due to their 
having both a subjective and an objective connotation. The two 
meanings of " efficiency " in the theory of wages should be carefully 
discriminated. 



Wages and Ability 73 

qualities, which is fehcitously summarized in the 
phrase "general sagacity and energy." 

Is there any ground for believing that this general 
theory has any relation whatever to the conditions 
of wage receiving in actual industry? Suppose the 
relevancy of the theory were- denied, — as indeed 
it is denied frequently and vehemently, — how could 
one proceed to *fortify it otherwise than by reverting 
to remote hypothetical premises and repeating the 
long chain of logical deductions ? If the theory is 
to be accepted as a law, using the word law in the 
sense of our first chapter, it must rest upon the 
concrete facts of industry. 

A similar position is to be assumed in approaching 
the explanation of wages from the inductive side. 
The conclusion upon this topic of the French Office 
du Travail, in its voluminous report on wages for 
1893-1897, is summarized in these words : " On 
voit entre quelles limites etendues varie la valeur 
relative du salaire dans les diverges professions. 
Cette valeur relative depend essentiellement de la 
rarete des aptitudes intellectuelles et physiques 
necessaires a I'ouvrier, du degre de developpement 
de ces m^mes aptitudes qu'exigent les diverses pro- 
fessions." ^ 

It is entirely true that one does see from the statis- 
tical schedules that there is a wide variation in rel- 
ative wao;es, but in the whole of the four volumes 
of the report there is not a word to show a quanti- 

1 Salaires et duree du travail dans l' Industrie franf:aise. Vol. I, p. 512. 



74 Laws of Wages 

tative relation between the amount of wages and 
" la rarete des aptitudes intellectuelles et physiques " 
of the laborer. So far as the use of words is con- 
cerned, administrative inquiry and pure theory take 
common ground. Would it be possible through the 
discovery of an economic law to bring the two to- 
gether so that the theory might organize the data 
and the data support the theory ? 

An Hypothesis as to the Distribution of Ability. 
Before we can establish a quantitative relation be- 
tween wages and ability we must have an hypothesis 
as to the distribution of ability among a representa- 
tive class of laborers. The particular hypothesis 
that is put forward in this chapter is that industrial 
ability — general sagacity and energy — is distrib- 
uted according to the normal or Gaussian law. 

The normal, or Gaussian, law is represented graph- 
ically in Figure 11 by either of the two curves 
AMB, amb. If from a homogeneous group of 
men a large number of measurements of any physical 
character are made, for exanjple of stature, it will 
be found that the measurements may be arranged 
in such a way that the relative frequencies of the 
deviations from the average measurement will, when 
plotted, produce a curve approximating this type. 
A deviation in excess of the average stature is 
measured to the right of point 0, on the line ox, 
and the corresponding frequency of the deviation 
is then plotted perpendicularly at the end of the 



Wages and Ability 



75 




I £ 



76 Laws of Wages 

deviation. Similarly, deviations below the average 
are measured to the left of point 0. The two 
sides of the curve are symmetrically disposed about 
the maximum ordinate, and the scatter of the meas- 
urements about this ordinate varies with the stand- 
ard deviation of the measurements. The standard 
deviation of the curve amh is twice that of the 
curve AMB. 

Grounds for the Hypothesis. 

In justification of the hypothesis that has just been 
described the following considerations are offered : — 

(1) The accumulation of a great number of meas- 

urements of physical characters, w^hich was 
begun by Quetelet and is now carried for- 
ward with zeal by anthropologists and bio- 
metricians, has established that physical 
qualities are distributed according to the 
Gaussian law. " We have very definite evi- 
dence that the normal curve suffices to de- 
scribe within the limits of random sampling 
the distribution of the chief physical charac- 
ters in man." ^ 

(2) Several years ago Sir Francis Galton began 

his studies of inheritance on the assumption 
that the mental and moral qualities of man 
are distributed according to the same law 
as are physical qualities. Professor Pear- 
son's laborious investigations of mental char- 

* Karl Pearson : Biometrika, Vol. II, p. 395. 



Wages and Ability 77 

acters proceeds upon the same assumption: 
" We have . . . selected, as the normal 
scale of intelligence, that which would be 
given if the frequency distribution of intelli- 
gence followed the normal, or Gaussian, 
curve of errors. Whatever the true scale 
may be, it can only be a more or less — prob- 
ably less — distorted form of this scale." ^ 
(3) It has been pointed out that industrial effi- 
ciency is dependent upon physical, mental, 
and moral qualities, and these qualities, ac- 
cording to tfie preceding paragraphs, there 
is good reason for regarding as being dis- 
tributed according to the Gaussian law. 
Professor Edgeworth has demonstrated a 
theorem to the effect that "... if a varia- 
ble thing obey the normal law, a function 
of that thing will obey the normal law." '^ 
Professor Edgeworth however gives the warn- 
ing that " this property holds only com- 
monly, not universally." 

^ Karl Pearson : Biometrika, Vol. V. p. 106. " An a priori justifica- 
tion of the scale may be found in the fact that the plotted points of 
the regression curves are for a nunaber of pairs of characters, within 
the limits of random sampling, on a straight line when such a scale 
of intelligence is used." Ibid., pp. 106-107. 

■^ Journal of the Royal Statistical Society, December, 1898, p. 676. 



7S Laws of Wages 

The Expression of the Gaussian Law in a Form that 
ivill facilitate the Testing of the Differential Theory 
of Wages. 

In the subsequent part of this chapter we shall 
refer to the theory concerning the law and cause of 
the distribution of general wages among the members 
of the labor group as the differential theory or the 
differential hypothesis of w^ages. 

The statement of the differential hypothesis by the 
most approved authorities contains four leading prop- 
ositions : — 

(1) The labor force in a country of varied indus- 

tries is a force of varying efficiency per la- 
borer unit ; 

(2) The character of the industrial organization of 

a particular time and place determines the 
nature and degree of segregation of laborers 
into groups of varying efficiency. The two 
most fundamental groups are those of skilled 
and of unskilled labor ; 

(3) The laborer of least efficiency in each group 

receives a wage which constitutes the mini- 
mum wage of the group. This minimum 
wage is not less than the hig-hest wasje that 
could be earned by the least efficient mem- 
ber of the group in the other forms of em- 
ployment w^iich are open to him ; 

(4) The more efficient laborers within a group re- 

ceive the minimum wage of the group plus 



Wages and Ability 79 

a supplement proportionate to the exce^ of 
their efficiency over that of the least capahle 
laborer in the same group. 

We have assmned that the distribution of abihty 
among a large group of laborers foUows the Gaussian 
law. But this law is a generalization applying to an 
infinite number of measurements, whereas the statis- 
tics of wages are aTailable for only a finite number of 
laborers. Furthermore, according to the differential 
hypothesis, wages are distributed among laborers 
proportionately to their differential ability. But the 
Gaussian law gives the law of the distribution of 
abOity for the aggregate of laborers : it do^ not de- 
scribe how the individuals in the aggregate differ from 
each other. It is therefore necessary to derive from 
the Cranssian law a formula that will be applicable to 
a finite group and will express the average differences 
in ability among the members of such a group. 

In 1902 Sir Francis Galton proposed to British 
mathematicians this problem : ^ A certain sum, say 
i£100. is available for two prizes to be awarded at a 
forthcoming competition ; the larger one for the first 
of the competitors, the smaller one for the second- 
How should the ^100 be most suitably divided be- 
tween the two ? What ratio should a first prize bear 
to that of a second one ? Does it depend on the 
number of competitors, and if so, in what way? 
Similiar questions may be asked . . . when the 
number of prizes exceeds two. What ^ould be the 



80 Laws of Wages 

division of the £100 when three prizes are to be 
given, or four, or any larger number ? " ^ Mr. Gal- 
ton's investigation suggested " that when only two 
prizes are given in any competition, the first prize 
ought to be closely three times the value of the 
second." The novelty and interest of the problem 
led him to conclude : " I now commend the subject 
to mathematicians in the belief that those who 
are capable, which I am not, of treating it more 
thoroughly, may find that further investigations will 
repay trouble in unexpected directions." 

Professor Karl Pearson answered the appeal to 
mathematicians and undertook the solution of the 
problem in this general form : " A random sample of 
n individuals is taken from a population of JV 
members which when JSf is very large may be taken 
to obey any law of frequency expressed by the curve 
y = N(f){x), ydx being the total frequency of individ- 
uals with characters or organs lying between x and 
x + dx. It is required to find an expression for the 
average difference in character between the p^^ and 
the {p + 1)''' individuals when the sample is arranged 
in order of mao;;nitude of the character." 

" I propose to call this general problem : Francis 
Gallons Individual Difference Prohlem in StatisticSy 
or, more briefly. Gallons Difference Prohlem. It will 
be seen at once to carry us from the consideration of 
the means and standard deviations of mass aggregates 

^ Francis Galton, F.R.S. : " The most Suitable Proportion between 
the Values of First and Second Prizes." Biometrika, Vol. I, p. 385. 



Wages and Ability 81 

and arrays to the average interval between individuals 
of those aggregates. We may still deal with averages, 
but we fix our attention no longer on the whole pop- 
ulation, but on definite individuals in its ordered array. 
This I believe to be a real advance in statistical 
theory." The solution of the problem " provides us for 
the first time, I believe, with most probable relation- 
'ships between individuals forming a random sample." ^ 
One would think that this mathenaatical problem 
had been formulated and solved with a view to the 
appHcation of the results to our problem of the dif- 
ferential hypothesis of wages ! For the knowledge 
of the average difference in ability between each of 
1000 laborers and his less efficient neighbor, when the 
whole number are ranked according to their ability, 
would afford data for determining the average dif- 
ference in ability of the 999 laborers over their least 
efficient associate. Moreover, if the 1000 laborers 
were separated into two groups, the one composed of 
the less efficient, and the other the more efficient, thus 
giving rise to a minimum wage in each group, the 
knowledge of the average difference in efficiency in 
the population of 1000 would suffice for the computa- 
tion of the average difference in efficiency of the 
members in each group over that of the least efficient 
member of the same group. To solve our problem of 
wages, the first need is the construction of a Standard 
Population in which the average differences in ability 

^ Karl Pearson : " Note on Francis Galton's Problem." Biometrika, 
Vol. I, pp. 390-399. 

G 



82 Laws of Wages 

of its members are computed. Such a Standard 
Population, judiciously used, would supply the means 
with which to obtain a first approximation to the 
solution of several questions in the dynamics of 
wages. 

The Standard Population. 

In the Appendix to this chapter are two mathe- 
matical tables: Table I, Average Differential Ability 
in a Population of One Hundred ; Table II, Standard 
Population of One Hundred. A detailed account of 
the construction of these tables is given in the Ap- 
pendix. Before proceeding to the description of 
Table II, upon which the investigation of this chapter 
is based, it may be observed that Table I enables us 
to answer the question as to the form of distribution 
of wages when the incomes of laborers are apportioned 
entirely according to ability. For example, in 1900, 
in the manufactures of the United States, the average 
wage of males over sixteen years of age was $ 11.43 
per week. The aggregate received by a population 
of 100 would therefore be $1143. Assuming the 
minimum wage to be $3.13 ^ then, if wages were dis- 
tributed entirely according to ability, each of the 
more sagacious and energetic laborers would receive 
the minimum wage $3.13, plus a supplement propor- 
tionate to his differential ability. That is to say, 99 
laborers would each receive $3.13 plus a share of 
$ 830 (1143 — 313), which would vary proportionately 

1 The reason for this assumption will appear later. 



Wages and Ability 83 

to the excess of his ability over that of the least capa- 
ble member of the group. The $830 would there- 
fore be distributed according to the conditions of 
columns IV and VIII in Table I. The ablest man 
would receive $3.13 plus (830) (.02) which is $3.13 
plus $16.60 =$19.73. Similarly, the wages of the 
other laborers would be ascertained. A graphic de- 
scription of the resulting distribution is given in the 
accompanying Figure 12, where wages are taken upon 
the axis of x and the relative frequencies of the sev- 
eral rates of wages are plotted parallel to the axis of 
y. The Gaussian curve traced upon the figure is 
practically an exact fit ^ to the data. 

Table II, The Standard Population of One Hundred, 
is designed to meet the difficulty of the segregation of 
labor, in actual industry, into groups of skilled and 
of unskilled labor. It is based upon the knowledge of 
the average differences in ability between members 
of a group of 100. The total population of 100 is 
divided into an upper group corresponding to skilled 
labor, composed of the fifty ablest members ; and a 
lower group corresponding to unskilled labor, com- 
posed of the less capable members. The two groups 
are then treated separately, just as the whole popula- 
tion was treated in Table I ; that is to say, each group 
of fifty is considered as forming a separate population. 
The average differences in ability of the fifty ablest 
members over the ability of the fifty-first member — 

1 According to the Pearsonian test, n^ = 17 and x^ — -94:2782, which 
is a perfect fit. 



84 



Laws of Wages 




05 <^ rv (0 "i * 



Wages and Ability 85 

who is the ablest member of the lower group — are then 
computed. Likewise the average differences in ability 
of the members of the lower group over the ability of 
the least capable member of that group are ascertained. 
In columns III and VII these differences are expressed 
in terms of the standard deviation of the group, and 
in columns IV and VIII the same individual differ- 
ences are respectively expressed as percentages of the 
sum of the differences. The method in which this 
table is used to bring to a statistical test the differ- 
ential hypothesis as to the distribution of wages will 
now be rendered clear by means of examples. 

The Application of the Tlieory of the Standard Popu- 
lation. 

Certain principles must be observed in selecting 
data to test the theory : — 

(1) The differential hypothesis is based upon the 
assumption of perfect competition of laborers. 
To meet this specification, (a) we have taken 
data only from adult male laborers in man- 
ufacturing industries, where competition 
among laborers is keenest, and (b) have 
made a supplementary hypothesis — designed 
to meet the difficulty of non-competing 
groups — to the effect that the labor force is 
divided into two groups, the members of 
each of which receive the minimum wage of 
their respective groups plus a supplement 
proportionate to their differential ability. 



86 Laws of Wages 

(2) The differential hypothesis is based on the 

assumption of conditions of wage earning 
in a limited area — " in neighboring places/' 
to use Professor Marshall's phrase. Ac- 
cordingly, in order to avoid complications 
of differences due to geographical separa- 
tion, the following data refer, as far as pos- 
sible, to conditions in homogeneous areas. 

(3) The differential hypothesis is based upon the 

assumption that opportunities for work are 
sufficiently varied to permit each laborer to 
exploit to the full his special degree of sa- 
gacity and energy. By confining the selec- 
tion of data to general manufactures instead 
of particular trades, this condition of the 
theory is approximated. 

We shall now consider in detail the application of 
the theory. 

{a) Wages in France. 

In Vol. I of the report of 1893 on Salaires et 
duree clu travail dans Vindustrie frangaise, p. 496, 
there is the following table giving the distribution 
of wages in the Departe7)ient de la Seine : — 



Wages and Ability 



87 



TABLE I. — DisTRiBUTiox of Laborers according to Rates 
OF Wages per Day. France 



Rate in Francs 


NuMBEtl 


Rate in Francs 


Number 


2.75 and less 


173 


7.25- 7.75 


1,3.59 


2.75-3.25 


137 


7.75- 8.25 


552 


3.25-3.75 


453 


8.25- 8.75 


232 


3.75-4.25 


1,172 


8.75- 9.25 


133 


4.25-4.75 


1,271 


9.25- 9.75 


76 


4.75-5.25 


2,182 


9.75-10.25 


137 


5.2.0-5.75 


1,351 


10.25-11.25 


30 


5.75-6.25 


1,551 


11.25-12.25 


15 


6.25-6.75 
6.75-7.25 


1,403 
1,-558 


More than 12.25 
Total 


19 


13,804 



This table describes the actual conditions of wage 
receiving among 13,804 representative workmen. 

In order to apply the differential hypothesis we 
must first settle upon the wage to be used as a mini- 
mum wage in the lower group of the Standard Popu- 
lation. The total range of the Standard Population 
of One Hundred is 5.02 times the standard deviation 
(2.52 + 2.50), which gives a half-range of 2.51 times 
the standard deviation. If, now, we refer to a table 
of the values of the probability integral in terms of 
the standard deviation, ^ we find that, on the average, 
six cases in a thousand exceed 2.51 times the stand- 
ard deviation. Consequently, in order to make the 
Standard Population of One Hundred applicable to 
the French schedule affecting 13,804 laborers, we 
have substracted from each end of the total series 
83 members, that is, (.006) (13,804). This would 

1 The best table is that of W. F. Sheppard : " New Tables of the 
Probability Integral." Biometrika, Vol. II, pp. 174-190. 



88 Laws of Wages 

leave 90 members in the lowest group and 118 in the 
group 9.75—10.25. If the lowest limit of actual 
wages be supposed to be 2 francs, we should then 
find the theoretical minimum for the Standard Popu- 
lation from the following proportion 173 : .75 : : 83 : cc. 
As X in this proportion is 36 centimes, the theoreti- 
cal minimum wage is 2.36 francs. Similarly, the 
superior limit of wages in the actual figures would 
be reduced to 10.18 francs. The modified schedule 
would then appear as in the first and second columns 
of the following table : — 



TABLE II. — Percentage Distribution of Laborers according 
TO Daily Rates of Wages in the Departement de la Seine 
AND IN the Standard Population 



Department de la Seine 


Standard Population 


I 


n 


III 


IV 


V 


Kale ill Francs 


Number 


Percentage 


liate in Francs 


Number 


2.55 
3.00 
3.50 
4.00 
4.50 
5.00 
5.50 
6.00 
6.50 
7.00 
7.50 
8.00 
8.50 
9.00 
9.50 
9.96 


90 

137 

453 

1172 

1271 

2182 

1351 

1551 

1403 

1558 

1359 

552 

232 

133 

76 

118 


.66 

1.00 

3.33 

8.59 

9.32 

16.00 

9.91 

11.38 

10.29 

11.42 

9.96 

4.05 

1.70 

.97 

.56 

.86 


2.36 
3.00 
3.50 
4.00 
4.50 
5.00 
5.50 
6.00 
6.50 
7.00 
7..50 
8.00 
8.50 
8.98 
9.31 
9.91 


1 

2 

4 

6 
10 
13 
14 
12 
11 

9 

7 

4.5 

3.5 

1 

1 

1 


Total 


13638 


100.00 


Total 


100 



Wages and Ability 89 

Having determined the theoretical minimum wage 
for the Standard Population, we now find by means 
of the first and third columns in the above Table II 
that the average wage in the manufactures of the 
Departement de la Seine was 5.864 francs per day, 
and that the first fifty per cent of the laborers — 
that is the less capable laborers — received 39.819 per 
cent of the total wage dividend. These three facts, 
to wit: (1) the theoretical minimum wage of the 
Standard Population (2) the average wage, and (3) 
the percentage of the wage dividend received by the 
less capable group, are all the facts that are neces- 
sary in order to apply at once the theory of differen- 
tial wages. 

We shall now proceed to determine what the dis- 
tribution would be according to the theory of reward 
in proportion to ability and shall then compare the 
theoretical distribution with the actual distribution. 

Since the average wage is 5.864 francs, the whole 
wage dividend to be shared by the Standard Popula- 
tion of One Hundred is 586.40 francs. As the less 
capable group receives 39.819 per cent of the total 
dividend, the first fifty members of the Standard Pop- 
ulation will divide between them 233.50 francs, and 
the more capable fifty will receive 586.40 — 233.50 = 
352.90 francs. The minimum wage in the less effi- 
cient group is 2.36 francs, and since, according to the 
differential hypothesis each of the fifty members of 
this group will receive the minimum wage of the 
group plus a supplement proportionate to his dif- 



90 Laws of Wages 

ferential ability, the total amount to be divided 
among the fifty laborers in the form of supplemen- 
tary payment is 233.50 - (50) (2.36) = 115.50 francs. 
The resulting distribution in this group will therefore 
be computed by means of column VIII in Table II 
of the Appendix to this chapter. For example, the 
fifty-first laborer — who is the ablest member of the 
less capable group — will receive 2.36 + (115.50) 
(.029083) = 2.36 + 3.3591 = 5.72 francs. In a simi- 
lar manner the amounts received by the other mem- 
bers of this group may be computed. 

The dividend of the more capable group is 352.90 
francs. The minimum wage of the group is the 
highest wage that could be earned in the lower 
group, which, as we have just seen, is 5.72 francs. 
This method of estimating the minimum wage of the 
more efficient group is regarded as in harmony with 
actual practice where the minimum wage in a group 
is equal to the highest wage that could be earned in 
other forms of employment open to the laborer. 

According to the differential hypothesis the mem- 
bers of the abler group receive likewise the minimum 
wage of their group plus a supplement proportionate 
to their differential ability. As the minimum wage 
is 5.72 francs, and the total amount shared is 352.90 
francs, the amount distributed in the form of sup- 
plementary payments is 352.90 -(50) (5.72) = 66.90 
francs. This sum 66.90 francs is distributed accord- 
ing to Table II of the Appendix, column IV. For 
example, the ablest member of the Standard Popula- 



Wages and Ability 91 

tion receives as total wage 5.72 + (66.90) (.062670) = 
5.72 + 4.1926 = 9.91. The fiftieth laborer receives 
5.72 + (66.90) (.000622) = 5.72 + .0416 = 5.76 francs. 
The wages of the other members of the more efficient 
group are computed in the same way. The resulting 
distribution of wages in the total Standard Popula- 
tion may be seen in columns IV and V of Table II 
printed in the text. 

To what degree is the differential hypothesis of 
wages borne out by the facts of wage receiving in the 
French Departement f If the figures in Table II for 
the actual distribution of wages in the Departement 
de la Seine and for the distribution in the Standard 
Population were plotted just as they are, it would 
be seen that the approximation is very close, but, 
because of the zigzag shape assumed by each series of 
figures, the measure of the degree of approximation 
would be rather vague. The result of the method 
which I have adopted to bring out the degree of ac- 
cordance between fact and theor}^ may be seen by 
referring to Figure 13. In this figure the zigzag 
line gives the actual percentage frequencies of wages 
as they appear between limits 2.36 and 10.18 in the 
French report. The dashed smooth curve, computed 
by Professor Pearson's method of moments, is the 
curve fittina; best the actual fio;ures. The continuous 
smooth curve is the best fit to the tabulated wages of 
the Standard Population. The fact that the smooth 
curve of the actual data is practically congruent with 
the smooth curve of the Standard Population shows 



92 



Laws of Wages 







































































































































































































































































































































































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Wages and Ability 93 

that in this particular case, a doctrine of pure econom- 
ics is statistically verified. " La valeur relative du 
salaire . . . depend essentiellement de la rarete des 
aptitudes intellectuelles et physiques necessaires k 
I'ouvrier, du degre de developpement de ces memes 
aptitudes qu'exigent les diverses professions." The 
words of the French report are now the accurate de- 
scription of an economic law. 

(b) Wages in Massachusetts. 

As the distribution of wages in the Departement de 
la Seine presents only a small degree of skewness, we 
shall offer a further test of the differential theory of 
wages by taking a case in which the distribution is 
characterized by a considerable degree of asymmetry. 
Table III of the text, which exhibits data for Massa- 
chusetts, has been constructed in a similar manner to 
that of Table II referring to the Devartement de Iq, 
Seine. The crude data of the table were taken from 
the Census of Manufactures, 1905, Bulletin 93, p. 109. 
Figure 14 illustrates the degree of correspondence 
between theory and practice. 

^emarh upon the Preceding Demonstration. 

The equal division of the Standard Population of 
One Hundred into two groups needs justification. 
The asymmetry of a wage curve is due to the influence 
of several factors, among which are the relative num- 
bers of laborers at different ages, the increasing value 
of high degrees of efficiency due to the increasing con- 



94 



Laws of Wages 







Wages and Ability 



95 



TABLE III. — Percentage Distribution of Laborers accord- 
ing TO Weekly Rates of Wages in Massachusetts and in 
THE Standard Population 



Massachusetts 


Standard Population 


I 


II 


III 


IV 


V 


Eate in Dollars 


Number 


Percentage 


Eate in Dollars 


Number 


2.79 


1414 


.44 


2..58 


1 


3.50 


4176 


1.29 


3.68 


1 


4.50 


8920 


2.75 


4.50 


2 


5.50 


13,937 


4.31 


5.50 


4 


6.50 


22,104 


6.83 


6.50 


6 


7.50 


28,055 


8.66 


7.50 


9 


8.50 


28,425 


8.78 


8.50 


11 


9..50 


39,951 


12.34 


9.50 


13 


10..50 


27,084 


8.36 


10.50 


8 


1L.50 


24,705 


7.63 


11.50 


7 


12.50 


22,239 


6.87 


12.50 


6 


13.50 


19,754 


6.10 


13.50 


6 


14.50 


17,216 


5.32 


14.50 


5 


15.50 


14,748 


4.55 


15.50 


5 


16.50 


12,603 


3.89 


16.50 


4 


17.50 


9958 


3.08 


17..50 


3 


18..50 


8098 


2..50 


18.50 


2 


19..50 


6203 


1.92 


19.50 


2 


20.50 


4541 


1.40 


20.50 


2 


21.50 


3164 


.98 


21.64 


1 


22.50 


2020 


.62 


22.81 


1 


23.50 


1162 


.36 


24.92 


1 


24.50 


1041 


.32 






25.50 


921 


.28 






26.50 


800 


.25 






27.40 


546 


.17 






Total 


323,785 


100.00 


Total 


100 



96 Laws of Wages 

centration of industry,^ the temporary monopoly of 
particular grades of skill, and the strategic advantage 
in bargaining enjoyed by trade-unions. It is not pos- 
sible at present to determine how far these factors 
are respectively effective in raising wages, and the 
equal division of the Standard Population into two 
groups is simply a means of giving expression to the 
joint effect of a number of factors whose individual 
influence has not yet been determined. It would be 
more philosophic but less simple to assume that this 
" joint effect " to the advantage of efficient laborers 
is a linear function of their differential efficiency. 

1 See Chapter VI. 



Wages and Ability 97 



APPENDIX 

Notes on the Construction of Table I. 

I. The table is composed of eight columns. Columns 
I and V, marked p-, give the rank of the individual in the 

total population of 100. Columns II and VI, marked — , 

give the difference between each individual and the next 
in order of rank divided by the standard deviation of the 
whole group. Columns III and VII give the difference, 
in terms of the standard deviation, between each individual 
of the group and the last member of the group. The first 
entry in column III is obtained by summing the entries in 
columns II and VI. The second entry in III is obtained 
by subtracting from the first entry in that column the first 
entry in column II. Similarly of the remaining entries in 
columns III and VII. Columns IV and VIII are obtained 
by expressing each entry in columns III and VII as a per- 
centage of the sum of the entries in columns III and VII. 
For example, the total of columns III and VII is 251.4425, 
and the first item in column III, 5.02885, is .02 of 251.4425. 

II. The mathematical derivation of — is explained in 
the "Notes on the Construction of Table II." 



98 



Laws of Wages 



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a, 


1— icicO'+Hiccot^cocR.O'HCico-tiiocot-ooajo^ 
lOiooioiOiooioiococococococococococoi-^t^ 


> 


a ^ 


0-+ICO.— iuticoo5eocoT-i-*co-#cDcoi>Tticoiococo 

OCOCOCDCOIQ'— (CI'Ot— lOOt^t-OOOCOt^T— ICOrHt^ 
O lO t^ rH t^ CO O t^ -f CI O t^ i.O CO CI O CO l^ >Q 'Tfi CI 
OCOI^t^COCOCOOlOlO-+l-*-^^-+l-^COCOCOCOCO 

ppppppppppppppppppopp 


s 


s § 
1 i 

CO Bh 


OCOCICOCOCIOSOClCO-flCOCOCOlO-tHCO'-HOCOCO 
iC CO CI 1^ Oi O lO CO O' O C;. -f >0 O 05 CI -^ CO O -ti -f 
CO GO CI -ti l^ CO CI -f CI CO CO lO >C CO CO 'O -ti 05 CO c: CI 
O) l^ l^ CI 1-- T-i t^ CO CO -H t- 1^ -t< t^ CI O CO CO O CO CO 

CI CO CO CI o .— 1 CI ira CO CI CO ^H CO ^H t^ '^1 CO -+I T— 1 1^ CO 
p o -^H CO CI i-i p p CO CO 1^ t^ o p >-0 iq -*H Tjj ^ CO CO 

kO-Tli-^Tji-^-^-^COCOCOCOCOCOCOCOCOCOCOCOCOCO 


- 


Difference 

Xp 

8 


'+l-HCOO'#COOiGOOiOiCOOOCOr-l,— ICIi— l-^OCO 

coiO'ttcooj-^oii.ooiOT^iojirai— (i^co-— co'QOco 

COO-Hi— IO5C0t--COCOl0>O-rl"^-TtH-ti-^C0C0COC0C0 

cociT-;.-Hppppppppppppppppp 


- 


- 


1— icicoTtiiccoi>.coa50i— icico-^iracot^cooso^H 

I-I.-IT— lrH.-HrHrHT-Hi-l.-HCICI 



Wages and Ability 99 



'^(CMOCOlOCMOJCDOiaDCOCOtMCOCi.— IC^J(Mr— IOO^t^iX)Tj<COOCOeO 
t^CDLOCOOI^HOSOOt^l-O-T^IC^.— tOil^CD-^CMOt^lOCMCIiCDfMOOCMT^ 

oooooooooooooooooooooooooooo 
oooooooooooooooooooooooooooo 



^T+ll:^lO(r>C0050Tt<'*005t^CDlOCMC^O)CDt~000'-MOO'*^00'* 
1— (Oi.Q'rOiOOSiOOJOOiraT— iOC^l'OTti020iC-Thi'-tHO:Ci-*i>Ot^'MCD 

COtOCOlO-^'— I02l0 0-*OOOJ001'^>— l'*'*T— I^OllOOt^T— (CDt— lO 
^^HCOlOCNaSLOGMOJLQ,— It^-^CSlO^^COi— ICDO-*t-0.— (C^OCDCD 
OS05000000t^l:^t^<:OQ3COlOiO^-^-*COCO(M(Mr-(0005COt^lOCO 



l:^(MOO-^i— ICOt^COt— 00.— ll0OC0CD(M01»-H0ilC'. OI'TflOOOSCDt^CDOS 
OOOt— (fMCMCO-*iiOCDC003T— (CM-^l^ClCOCD.-Ht^-TtiCCi-O-^'^tOO 

OOOOOOOOOOOOOOOOOOOOOOOO.— It— lOlOO 



l^t^t^l^t^t-t^t^OOCOaOOOCOQOCOCOOOGOCiOSOiOiCOCiClOiOSOS 



CO^COOOt^t^OlCOCOCO^iOCDaiCMt^COOlCD^CM.— (005C»C»OiO 

CO O t- Ji CI Oi t^ lO ^ C-1 T— I O CD GO t:^ t^ !» CO iC lO lO O O lO ^ Tti 'rti ■* lO 

T— lOCOt^CO'^COOjT— lOCiCOOira^COCMi— (OCSCDl^CDLO-rflCOCMT— lO 
C0C0C.1OJC>IC)(MO)(M(Mt— I^Ht— ii— irH^HT-tT— It— lOOOOOOOOOO 

T— IrHl— It— Ir-ll— It— iT-li— It— It— ItHt— It— l>— IrHi— It— (1— li— 11— It— It— It— It— li— I'l— (1— (.— I 

ooooooooooooooooooooooooooooo 



Ot— (■Tt^'^lOcocDco05■"#l:^o«503l.!:5 0'^•r^^co(^JO^-oi>.ooi^^oc^co 
<r>cDOoi.— lOiTticooit^cio-TtiiocoTtiiocscoioc^icot^c^jioascocoira 
lO 1^ CO o (M CO T— I ■* oj -^ t— 1 T— I iQ CI c^] o o r-- r^co^Hioot^-^c^ii— loc^ 

C0CSCD'*IC0CM(M(MC0-^i»00OC0CDO5C0COO-ti0iC0C0 01t^0al-^0)C0 

ococoot^^T— icoioojoico^T— ico>-racoocoiO(MOt^iorMOi--iocj 
cooiOJOiT-jT— It— iooociosoic^oqcocqa3i~--i--;»--;i--;<:DCD':DCD>OLOio 

CO CO CO CO CO 00 CO CO CO CO (^i oi (^^ ci oi oi cj oj oi c4 oj <>i oi O) (^^ c^ oa oi (>i 



oit^ool<^ll:^o^^lOt^^^T^^l:^-*ocooT-l,— icMcoco^ooit^co-^ico 

COCOCOt^Ol-T+iT— (OiO-^COt— l0005CMCX)CC>COCOCOOOlO»OCDC&COCRl--5g 
t^CDT— i-^COOlt^fMr-COCOCOtMOSt^-rhliMOCOt^iO-^COOlT^'— lOOO 
CO (M Ol T— I O O 05 Oi 00 CO t^ t^ t^ CD CD 03 CO CO l-O l-O lO l-O lO >0 lO lO VO lO IQ 
CO CO CO CO CO CO CM CM (M (M (M (Ol OJ O) <M Ol CI Ol OI CI <M CM Ol (M CM CM C] Ol CM 
OOOOOOOOOOOOOOOOOOOOOOOOOOOOO 



CM«0-*ir5COt^COC350T— IdCO'TtllOCDt^OOOSO'— ICMCO'!*<>C3CD1>-C020 
CMdCMlMCMCMCMCMCOCOCOCOCOCOCOCOCOCO-*-*-^'^'*-^-^'*'*''^'" 



100 Laws of Wages 

Notes on the Construction of Table II. 

I. The table is composed of eight columns. Columns 
I and V, marked jt?, give the rank of the individual in the 

total population of 100. Columns II and VI, marked ^, 

give the difference between each individual and the next 
in order of rank, divided by the standard deviation of the 
whole group. Column III gives the difference, in terms 
of the standard deviation, between each of the first fifty 
members of the group and the fifty-first member. The 
first entry in the column is obtained by summing the en- 
tries in column II. The second entry in column III is ob- 
tained by subtracting from the first entry in that column 
the first entry in column II. Similarly of the remaining 
entries in column III. Column VII is constructed from 
column VI in the same way that column III is constructed 
from column II. Column IV is obtained by expressing 
each entry in column III as a percentage of the sum of 
the entries in column III. Similarly column VIII is con- 
structed from column VII. For example, the total of 
column III is 40.321478, and the first item in column III, 
2.526958, is .06267 of 40.321478. 

II. In computing the successive differences between 
the first six members of the Standard Population, Pro- 
fessor Pearson's formula for ^^ was used. 

where s is the standard deviation. (See Biometrika, Vol. 
I, p. 396, formula XXVII.) 

III. Since, by Stirling's formula, when p is large, 

\p= V27rppPe-P, the factor X?^!^Z!l^, in the above for- 



Wages and Ability 10 i 

mula for %^, approximates to unity with increasing values 
of p. The last factor, {1 4- <?i + ^2 + ^3 ••'!' seems also to 
approach unity as p increases. When p = 5, 

V^irppPe-p 5 1 + . + c . . ...| = .989794. 

It has consequently been thought sufficient for the pur- 
poses of this chapter to compute Xp ^7 the formula 

%„= for the values of p greater than 5 and less 

than 51. 

IV. The values of m, which were needed to obtain ^^, 

were computed from the formula ^ =-./_) e-^^^dx. 

n Xtt-^o 

(JIbid., p. 395, formula XII.) In making these compu- 
tations the values of the probability integral as given in 
Merriman's Least Squares were used. The table was 
computed several years ago when I was not acquainted 
with the apparatus for making easy and accurate calcula- 
tions. The values of m and y^ could be obtained simul- 
taneously from Sheppard's Tables (^Biometrika, Vol. 11, 
pp. 174-190), by using the formulae 

n-p r+"» 1 ,,-, , 1 

^ = I — = e~^^ dx, and v^ = — =: e^™ . 

{Biometrika, Vol. I, p. 395.) 

V. The degree of accuracy of the table is not so great 
as it appears to be because, in the evaluation of m, Bar- 
low's tables were employed in the calculation of squares, 
and consequently only four figures were used. This de- 
fect does not in any degree invalidate the theoretical 
result that has been reached, but it is noted here as a 
warning to others who, otherwise, might use the table for 
a purpose requiring greater precision. That it is practi- 



102 , Laws of Wages 

cally accurate for present purposes follows from the fact 
noted in the chapter that when the distribution of wages 
is calculated by Table I the resulting smooth graph is a 
Gaussian curve. The degree of fit, when subjected to the 
Pearsonian test, gives n' = 17 and X^= .942782, which is 
practically a perfect fit. 



Wages and Ability 



103 



TABLE II — Standard Population of One Hundred 


I 


II 


III 


IV 


V 


VI 


VII 


VIII 




Diflferenoe 


Difference 


Percentage 




Difference 


Difference 


Percentage 


P 


M. 


from the 


of 


P 


Xp 


from tlie 


of 




s 


51st Person 


40.321478 




s 


100th Person 


86.026422 


1 


.360964 


2.526958 


.062670 


51 


.025074 


2.501892 


.029083 


2 


.200664 


2.165994 


.053718 


52 


.025098 


2.476818 


.028791 


3 


.144746 


1.965330 


.048741 


53 


.025137 


2.451720 


.028500 


4 


.114680 


1.820584 


.045152 


54 


.025192 


2.426583 


.028207 


5 


.095994 


1.705904 


.042308 


55 


.025266 


2.401391 


.027915 


6 


.083843 


1.609910 


.039927 


56 


.025354 


2.376125 


.027621 


7 


.074499 


1.526067 


.037847 


57 


.025458 


2.350771 


.027326 


8 


.067258 


1.451568 


.036000 


58 


.025583 


2.325313 


.027030 


9 


.061599 


1.384310 


.034332 


59 


.025732 


2.299730 


.026733 


10 


.056909 


1.322711 


.032804 


60 


.025881 


2.273998 


.026434 


11 


.053146 


1.265802 


.031393 


61 


.026061 


2.248117 


.026133 


12 


.049990 


1.212656 


.030075 


62 


.026260 


2.222056 


.025830 


13 


.047250 


1.162666 


.028835 


63 


.026486 


2.195796 


.025525 


14 


.044913 


1.115416 


.027663 


64 


.026725 


2.169310 


.025217 


15 


.042871 


1.070503 


.026549 


65 


.026994 


2.142585 


.024906 


16 


.041081 


1.027632 


.025486 


66 


.027287 


2.115591 


.024592 


17 


.039512 


.986551 


.024467 


67 


.027614 


2.088304 


.024275 


18 


.038131 


.947039 


.023487 


68 


.0279(57 


2.060690 


.023954 


19 


.036854 


.908908 


.022542 


69 


.028347 


2.032723 


.023629 


20 


.035700 


.872054 


.021628 


70 


.028755 


2.004376 


.023300 


21 


.034686 


.836354 


.020742 


71 


.029207 


1.975621 


.022965 


22 


.033769 


.801668 


.019882 


72 


.029710 


1.946414 


.022626 


23 


.032937 


.767899 


.019044 


73 


.030247 


1.916704 


.022280 


24 


.032160 


.734962 


.018228 


74 


.030822 


1.886457 


.021929 


25 


.031479 


.702802 


.017430 


75 


.031479 


1.855635 


.021571 


26 


.030822 


.671323 


.016649 


76 


.032160 


1.824156 


.021205 


27 


.030247 


.640501 


.015885 


77 


.032937 


1.791996 


.020831 


28 


.029710 


.610254 


.015135 


78 


.033769 


1.759059 


.020448 


29 


.029207 


.580544 


.014398 


79 


.034686 


1.725290 


.020055 


30 


.028755 


.551337 


.013674 


80 


.035700 


1.690604 


.019652 


31 


.028347 


.522582 


.012960 


81 


.036854 


1.654904 


.019237 


32 


.027967 


.494235 


.012257 


82 


.038131 


1.618050 


.018809 


33 


.027614 


.466268 


.011564 


83 


.039512 


1.579919 


.018366 


34 


.027287 


.438654 


.010879 


84 


.041081 


1.540407 


.017906 


35 


.026994 


.411367 


.010202 


85 


.042871 


1.499326 


.017429 


36 


.026725 


.384373 


.009533 


86 


.044913 


1.456455 


.016928 


37 


.026486 


.357648 


.008870 


87 


.047250 


1.411542 


.016408 


38 


.026260 


.331162 


.008213 


88 


.049990 


1.364292 


.015859 


39 


.026061 


..304902 


.007562 


89 


.053146 


1.314302 


.015278 


40 


.025881 


.278841 


.006915 


90 


.056909 


1.261156 


.014660 


41 


.025732 


.252<)()0 


.006274 


91 


.061599 


1.204247 


.013999 


42 


.025583 


.227228 


.005635 


92 


.067258 


1.142648 


.013283 


43 


.025458 


.201645 


.005001 


93 


.074499 


1.075390 


.012501 


44 


.025354 


.176187 


.004370 


94 


.083843 


1.000891 


.011635 


45 


.025266 


.150833 


.00.3741 


95 


.095994 


.917048 


.010660 


46 


.025192 


.125567 


.003114 


96 


.114680 


.8210.54 


.009544 


47 


.025137 


.100375 


.002489 


97 


.144746 


.706374 


.008211 


48 


.025098 


.075238 


.001866 


98 


.200644 


.5(il628 


.006529 


49 


.025074 


.050140 


.001244 


99 


.360964 


.360964 


.004196 


50 
Total 


.025066 


.025066 


.000622 










2.526958 


40.321478 




Total 


2.501892 


86.026422 





CHAPTER V 

WAGES AND STRIKES 

" Ce ne sont pas les greves qui rendent compte des variations du 
salaire, soit par leur succes, soit par leur ^chec, mais ce sont les causes 
r6elles de variation du salaire qui se manifestent par une part dans 
les greves et rendent compte de I'existence, de la place et des r6sultats 
de ces greves memes." 

— Francois Simiand. 

In the investigation of the critical question of 
modern industry concerning the relation of wages to 
strikes, neither of the extreme theories as to the 
nature of that relation will be adopted as an exclu- 
sive working hypothesis. The wage-fund theorists 
will not be followed in their assumption that the rate 
of wages is determined by inexorable economic laws, 
and that organizations of laborers for the purpose of 
increasing wages must at best be ineffectual, while as 
a rule they would prove harmful. Nor will the mili- 
tant syndicalist be followed in the assumption of an 
unlimited power of labor organizations to better the 
economic status of the laborer. The one hypothesis 
that is entertained is that both economic law and trade 
combinations affect the outcome of trade disputes as 
to wages, and the scientific task that is imposed is to 
measure, as far as possible with available data, the 
relative importance of the two factors in the deter- 
mination of the resulting rate of wages. 

104 



Wages and Strikes 105 

Preceding chapters have shown, not theoretically 
but concretely, that wages move pari passu with the 
productivity of labor, and that the productivity of 
labor is conditioned by the degree and nature of the 
organization of capital and labor in industry. Does 
the productivity of labor likewise set bounds to the 
power of labor organizations to raise wages ? Does 
the productivity theory of wages give a clew to regu- 
larities in the outcome of strikes ? Are there economic 
laws of strikes ? 

In this chapter an attempt will be made to obtain 
some definite idea as to the power of trades-unions to 
raise wages and as to the limits set by economic law 
to the effective activity of trades-unions. The in- 
quiry will consequently seek answers to two questions : 

(1) as to the manner and measure in which trades- 
unions influence the outcome of trade disputes ; and 

(2) as to the manner and measure in which the out- 
come of trade disputes is limited by economic law. 

Outcome of Strikes as affected hy Trades- Unions. 

If it be true that labor organizations exert an in- 
fluence on the outcome of strikes, then the following 
conclusions would seem to be necessary corollaries : 
(1) The outcome of strikes that are declared by labor 
organizations should be more favorable to the interests 
of laborers than the outcome of strikes that are not 
so declared ; (2) The stronger the labor organization 
in an industry, the more favorable to the interests of 



106 



Laws of Wages 



the laborer should be the outcome of strikes that are 
declared by labor organizations in the industry. 
These two conclusions we shall test with the avail- 
able data. 

The material used in the treatment of most of the 
topics discussed in this chapter may be found in the 
volume on Strikes and Lockouts that was issued, in 
1906, as the Twenty-First Annual Report of the Com- 
missioners of Labor, for the United States. This 
volume will be referred to, simply, as the Report. 



TABLE I. — Correlation bktween the Outcome of Strikes 
AND the Ordering or not Ordering of Strikes by Labor 
Organizations 





OiTTcoME OP Strikes 
Establishments in which Strikes 


Total 


Succeeded 


Succeeded 
Partly 


Failed 


Ordered by 

Labor 

Organizations 


80,772 


25,916 


56,563 


163,251 


Not ordered 

by Labor 

Organizations 


5927 


1720 


9857 


17,504 


Total 


86,699 


27,636 


66,420 


180,755 



Table I of the present chapter, which was compiled 
from pages 490-491 of the Report, presents material 
pertinent to an investigation as to whether the results 
of strikes ordered by labor organizations are more 
favorable to the interests of laborers than the results 



Wages and Strikes • 107 

of strikes that are not so ordered. The table gives a 
summary of the results of strikes in the United States 
from 1881 to 1905. 

The method that is employed to measure the rela- 
tion between the two variables — the outcome of 
strikes and the ordering or not ordering of strikes 
by labor unions — is the method that has recently 
been invented by Professor Pearson ^ for the evalua- 
tion of the " correlation ratio," which is symbolized 
by the Greek letter rj. The method is applicable 
to problems like the one presented in Table I, on 
condition that one of the variables may be assumed 
to be distributed according to the Gaussian law. 
The method affords a good first approximate measure 
of relation when the distribution of the variable is 
slightly skew. The arithmetical value of t], like the 
coefficient of correlation, varies from zero to unity. 

In making the computation in the particular case 
of Table 1, it has been assumed that the alternative 
variable — " ordered by labor organizations " and 
"not ordered by labor organizations" — is distrib- 
uted according to the normal law. Some justifica- 
tion of the assumption is found in the definition of 
the terms by the Bureau of Labor. " The number 
of strikes ordered by labor organizations includes 
all strikes ordered by direct vote of a labor organi- 
zation and also all ordered by a business agent or 

1 Biometriha, Vol. VII, pp. 248-257. " On a New Method of 
determining Correlation when One Variable is given by Alternative 
and the Other by Multiple Categories." 



108 • Laws of Wages 

committee of such organization acting under powers 
conferred by the organization." Report, p. 109. 
" The strikes that are tabulated as not having been 
ordered by labor organizations are not necessarily 
strikes begun and carried on by employees who were 
not members of an organization. They include not 
only this class of strikes, but also strikes carried on 
by members of organizations, when these strikes were 
without the authority of such organizations." Report, 
p. 31. 

The value of rj computed on the assumption that 
the alternative variable is normal in its distribution 
is .218. The conclusion is therefore justified that 
the results of strikes ordered by labor organizations 
are more favorable to the interests of laborers than 
the results of strikes that are not ordered by labor 
organizations. The degree of association between 
the two variables is, however, rather low, and is 
measured by 17 = .21 8. 

The second inquiry concerning the influence 
exerted by labor organizations on the outcome of 
strikes may be worded as follows : To what degree 
is it true that the stronger the labor organizations 
in an industry, the more favorable to the interests 
of the laborers are the results of strikes that are 
declared by labor organizations in the industry ? 
In order to obtain an answer to this question, it will 
be necessary to agree upon some measure of strength 
in labor organizations, and to array the various 



Wages and Strikes 109 

industries of the country in the order in which labor 
organizations are strong, in respect to the quality of 
strength that is agreed upon. 

From one point of view, the strength of labor 
unions may be measured by the degree in which 
the trade disputes in an industry are ordered by 
trades-unions. If a large proportion of the strikes 
in an industry have their origin outside of the trades- 
unions, it may be assumed, as a general rule, not 
only that trades-unions are not strong when the 
industry is considered as a whole, bnt that the unions 
in the organized part of the industry are not strong. 
The fighting capacity of the organized part of the 
industry must be weakened, as a general rule, by 
the existence of a large body of unorganized laborers 
in kindred occupations of the same industry. 

When the strength of trades-unions is measured 
by the degree in which the strikes in an industry are 
ordered by trades-unions, is there any relation be- 
tween the strength of the unions and the outcome of 
strikes ordered by the unions ? 

On pages 33-34 of the Keport on Strikes and 
Lockouts a table is given of " Strikes and Establish- 
ments involved in Strikes ordered by Labor Organ- 
izations and not so ordered, by Industries, 1881 to 
1905." This table supplies material for ranking the 
82 enumerated industries according to the percent- 
ages of total strikes, in the several industries, that 
were ordered by labor organizations. For example, 
in the industry for the manufacture of agricultural 



110 Laics of Wages 

implements, labor organizations declared 63.22 per 

cent of all the strikes affecting that industry between 
the years 1881 and 1905 inclusively. It is assumed 
in tlie subsequent argument (1) that the control of 
trade disputes of an industry on the part of labor 
unions is proportional to the percentage of total 
strikes aft'ecting the industry that are declared by 
labor unions; (2) that the strength of the labor 
organizations of a particular industry is proportional 
to tlieii- control of trade disputes. 

On pages 486-487 of the same Report there is 
given a table headed, '• Summary of Strikes for the 
United States, ordered by Labor Organizations and 
not so ordered, by Industries, 1881 to 1905." The 
same 82 industries that appeared in the table which 
has just been described are enumerated also in the 
above '• Summary." Furthermore, this '' Summary " 
gives the outcome of strikes that were ordered by 
labor org-anizations, according as the strikes sue- 
ceeded, succeeded partly, or failed. 

From these official data Table II has been con- 
structed. The table will afford the means of meas- 
uring the relation between the degree in which labor 
unions control trade disputes and the outcome of 
strikes ordered by unions. That is to say, the table 
will supply an answer to the question as to whether 
the outcome of a strike ordered by labor organiza- 
tions is in any way associated with the measure in 
which the labor organizations control the trade dis- 
putes of the industry. If the hypothesis is accepted 



Wages and Strikes 



111 



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112 Laws of Wages 

that the strength of labor organizations is propor- 
tional to their control of trade disputes, Table II will 
likewise supply an answer to the question as to 
whether the strength of labor organizations has any- 
thing to do with the outcome of strikes declared by 
org;anizations. 

The construction of the talkie will be made clear 
by an illustration. In the first column of the body 
of the table marked " Below 20," the figures 389 
signify that, in all of the industries covered by the 
official report, 389 establishments in which strikes 
occurred were in industries in which labor organiza- 
tions declared below 20 per cent of the total strikes 
of the industry. In case of 211 of these 389 estab- 
lishments the strikes failed ; in 67 of the establish- 
ments the strikes were compromised; and in 111 of 
the establishments the strikes succeeded. It will be 
observed that the table refers only to the outcome of 
strikes ordered by labor organizations. All of the 
data in the official summary have been included ex- 
cept the material referring to " domestic service " and 
to " miscellaneous." 

From this table two conclusions will be drawn: (1) 
as to the nature of the association between the out- 
come of strikes and the degree of control of trade 
disputes on the part of labor organizations, and (2) as 
to the measure of this relation. 

The method employed in extracting the conclusions 
from the data is the method invented by Professor 
Pearson for the derivation of the coefficieut of mean 



Wages and Strikes 113 

square contingency. An indication of the significance 
of the coefficient of mean square contingency, as a 
measure of association, is given by the following con- 
sideration : The total number of establishments in 
which strikes occurred is seen, from the entry in the 
next to the last column and the bottom row, to have 
been 156,459. Of this total number of establishments 
53,512 were establishments in which the strikes 
failed ; 24,943 were establishments in which the 
strikes succeeded partly ; and 78,004 were establish- 
ments in which the strikes succeeded. The last column 
marked " Chances " gives the ratio of these numbers, 
respectively, to the total number 156,459. If, now, 
the outcome of the strikes in the 389 establishments 
recorded in the first column had been similar to the 
outcome in the whole of the establishments enumerated, 
the number of the establishments in which the strikes 
failed would have been (389) (.3420193) = 133.05 ; 
the number in which strikes succeeded partly would 
have been (389) (.159422) = 62.02 ; and the number 
in which strikes succeeded would have been (389) 
(.4985587) =193.94. Numbers derived in this way 
will be referred to as the numbers given by inde- 
pendent probability. 

Now it is clear that the numbers actually occurring 
in the subgroups differ from those given by inde- 
pendent probability. In case of the establishments 
in which strikes failed, we have in the first column 
211-133.05= +77.95. And in case of the estab- 
lishments in which strikes were successful, we have 



114 Laws of Wages 

111 - 193.94 = - 82.94. That is to say, in industries 
in which labor organizations were weakest, — in the 
sense of controlUng only a small percentage of the 
strikes that occurred in the industries, — the outcome 
of strikes, in establishments in which strikes occurred, 
was such that there was a positive deviation from 
independent probability of +77.95 in case of strikes 
that failed ; while, in case of strikes that succeeded, 
there was a negative deviation from independent prob- 
ability equal to - 82.94. 

If, in a similar manner, the column marked " Above 
80 " is examined, it will be found that, in case of 
establishments in which strikes failed, there is a neg- 
ative deviation equal to — 5809.57, while, in establish- 
ments in which strikes succeeded, there is a positive 
deviation equal to 7888.86. 

We find, therefore, that for weakly organized in- 
dustries, the successes are fewer and the failures are 
more than would be given by independent probability ; 
while for strongly organized industries the contrary 
relation proves to be true. These two extreme 
columns suggest that the outcome of a strike is in 
some manner related to the degree of union control 
of the industry, and it is required to determine rigidly 
from all of the data of the table the quality and the 
degree of association betw^een the two variables. 

The deviations from the independent probability of 
the same sign, or some function of the deviations may 
be taken as a measure of the association. But, as in 
other forms of relation the coefficient of correlation 



Wages and Strikes 115 

has been used to measure the degree of association, it 
is desirable — in order that types of association like 
that with which we are dealing may be compared 
with types in which the coefficient of correlation is 
the appropriate measure of association — to choose 
from the many possible functions of deviations from 
independent probability such a function that, in case of 
normal distribution where the two methods may be 
applied, the measure of association remains the same, 
whether it is computed by the newer method or by the 
method of the coefficient of correlation. The coeffi- 
cient of mean square contingency, which is a function 
of the squares of the deviations from independent 
probability, and the coefficient of mean contingency, 
which is a function of the deviations of the same sign, 
are two functions that fulfill the above conditions. 
If the former coefficient be represented by C^ and the 
latter by C2, then, in case of normal distribution when 
all three methods may be applied, 0^= C.2 = r, where r 
is the coefficient of correlation. The range of value 
of Ci and C2 is from zero to unity. Their signs must 
be determined by special methods.^ 

When the association or contingency between the 
degree of union control of strikes and the outcome of 
strikes is computed from our Table II by means of 
the contingency coefficients, we obtain for the coeffi- 
cient of mean square contingency (7i = .232 ; and 
for the coefficient of contingency €2= .30. 

1 Karl Pearson : On The Theory of Contingency and its Relation 
to Association and Normal Correlation. 



116 Laws of Wages 

The conclusions from the investigation are, there- 
fore: (1) The greater the degree in which labor 
organizations control the disputes of an industry, the 
more likely is the outcome of a strike declared by 
labor organizations to be faA^orable to the interests of 
laborers ; (2) The measure of the association between 
the degree in which labor unions control trade disputes 
and the outcome of strikes declared by organizations 
is C, = .232 and C, = .30. 

Figure 15 illustrates the association between the 
two variables. The diagram is constructed ork the 
assumption that the variable which measures the out- 
come of strikes is distributed according to the normal 
law.^ The origin is taken at a line separating estab- 
lishments in which strikes " succeeded partly " from 
establishments in which strikes " failed." The zig- 
zag line is the line of the means of the respective cate- 
gories. It is seen that the mean outcome of strikes, in 
industries in which below 20 per cent of the strikes were 
called by labor organizations, was a failure ; while in 
industries in which above 80 per cent of the strikes 
were called by labor organizations, the mean outcome 
of strikes was a success. As the degree of control of 
trade disputes by labor organizations increases, the 
general trend of the mean outcome of strikes moves 
from failure, through compromise, to success. 

There is need of great caution in the interpretation 

1 Let it be observed that no point in the argument is dependent 
■upon this assumption. This form of diagram was invented, I believe, 
by Professor Pearson. 



Wages and Strikes 



117 






s; 



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I 



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o 6 






118 Laws of Wages 

of these results. It is not to be inferred that the 
relation between the strength of labor unions and the 
outcome of strikes is a relation of cause and effect. 
The low value of C^ precludes the hypothesis of a 
direct cause and effect relation. The two phenomena 
may be joint effects of a common cause. Moreover, 
the results have been determined from data as to all 
industries and as to all causes. The mixing of the 
material in this manner introduces an element into 
the problem the influence of which it would be dif- 
ficult to measure. Suppose that the outcome of strikes 
is dependent upon the nature of the particular causes 
for which the strikes are called, that is to say, suppose 
that the probabilities of the outcome of strikes being 
in favor of the laborers vary according to the nature 
of the causes. Then, if labor organizations in weakly 
organized industries are predisposed to strike for 
causes that are likely to fail, while the stronger unions 
enter into trade disputes for more promising causes, 
the results that we have obtained would find their 
explanation not in the degree in which labor unions 
control trade disputes, but in the wisdom with which 
strong unions choose the grounds of the disputes into 
which they enter. 

Before taking up these considerations, we may note 
another relation that has a bearing upon the outcome 
of strikes, as far as the outcome is affected by the 
strength of labor organizations. Is the result of a 
strike the more likely to be favorable to the interest 
of the laborers, the greater the length of time the 



Wages and Strikes 



119 



laborers hold out ? Or is the contrary the case ? If 
the duration of a strike and its outcome are either 
directly or inversely related, what is the measure of 
the degree of association between the two ? 



TABLE III. — Contingency between the Duration of Strikes 
AND THE Outcome of Strikes. Germany, 1899-1905 







L»AYS OF DuKATlOiV 


Total 




1-5 


6-10 


11-20 


21-30 


31-60 


61-100 


101 or 

over 


H 
H 

S 

H 

O 

a 
m 
a 

to 


Succeeded 


1134 


353 


275 


122 


80 


57 


14 


2035 


Succeeded 
partly 


1106 


601 


577 


364 


336 


299 


124 


3407 


Failed 


1563 


598 


517 


344 


434 


438 


181 


4075 


Total 


3803 


1552 


1369 


830 


850 


794 


319 


9517 



TABLE IV. — Contingency between the Duration of Strikes 
AND the Outcome of Strikes. France 1890-1905 







Days of Duration 


Total 




7 or 

under 


8-15 


16-30 


31-100 


101 or 

over 


< 

s 

H 
CO 

O 
BS 
« 

to 


Succeeded 


1522 


285 


132 


98 


4 


2041 


Succeeded 
partly 


1665 


618 


379 


328 


36 


3026 


Failed 


2131 


613 


337 


337 


51 


3469 


Total 


5318 


1516 


848 


763 


91 


8536 



120 Laws of Wages 

Tables ^ III and IV, referring respectively to the 
history of strikes in Germany from 1899 to 1905, and 
to the history of strikes in France from 1890 to 1905, 
supply material for answering these questions. In 
case of the figures for Germany C^ = .22; C, = .26. In 
case of the figures for France, C^ = .16; C.^ = .19. 

It may be concluded that — 

(1) the greater the duration of the strike, the less 

likely is the outcome of the strike to be favor- 
able to the interests of the laborers ; 

(2) the measure of the association between the 

duration of strikes and the outcome of strikes 
is, in case of Germany, C-^ = .22 ; in case 
of France, (7i = .16. 

Here again caution in the interpretation of the 
results is very necessary. Is it to be inferred from 
the above conclusions that protracted strikes tend to 
end contrary to the interests of laborers because the 
greater duration of the struggle exhausts the funds 
of trades-unions and weakens their fighting capacity ? 
The inference is not warranted by the data. The 
low coefficients of contingency suggest the unwisdom 
of drawing any conclusion from the data as to cause 
and effect. Besides, the lumping of the results of all 
causes of strikes leaves room for an indefinite number 
of hypotheses as to the specific cause of the relation 
that has been established. May it not be true that 

^ The tables are taken from the Report for 1906 on Strikes and Lock- 
outs, pp. 859, 840. 



Wages and Strikes 121 

strong unions, when they do enter into trade disputes, 
strike for causes that are likely to end quickly in the 
interests of the laborers, while the weaker unions vainly 
protract their disputes through ignoring economic 
laws in the choice of the time and grounds of their 
strikes ? 

Outcome of Strikes as Limited hy Econom,ic Law. 

This discussion brings us to the consideration of 
the role of economic law in determining the out- 
come of strikes. In searching for the influence of 
economic laws in this particular field the first ques- 
tion that one is led to ask takes this form : Is the 
outcome of a strike, so far as the interests of the 
laborers are concerned, independent of the nature 
of the cause of the strike ? This question may 
be put more concretely. The Bureau of Labor of 
the United States classifies strikes according as they 
had their origin in one or more of fourteen causes. 
Is it found, from the record of the Bureau, that 
strikes succeed, succeed partly, or fail in the same 
proportion of cases, no matter what the cause of 
the strikes may be ? Or is it true that certain 
causes of strikes are more likely to lead to success- 
ful issues than other causes ? The answering of 
these questions will put one in the way of con- 
necting the outcome of strikes with economic causes. 

Table V, which was compiled from the Report on 
Strikes and Lockouts, p. 63, makes possible the 
computation of the contingency between the causes 



122 



Laws of Wages 



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Wages and Strikes 123 

of strikes and the outcome of strikes. The table 
includes the results only of strikes that were under- 
taken for single causes; it does not deal with the 
results of strikes in which the causes were mixed. 

The computation of the contingency coefficients 
gives C, = .298 ; C, = .33. With these values defi- 
nitely ascertained, it cannot be denied that the out- 
come of a strike is associated with the kind of cause 
for which the strike is undertaken. 

From Table Y, it is also possible to derive values 
that will throw light upon the ranking of causes 
according as they are the origin of strikes that are 
likely to succeed, to succeed partly, or to fail. If 
the percentage deviations of the actual figures in the 
subcontingency groups are computed from independ- 
ent probability, then the magnitudes and signs of 
the percentages will supply indices of the rank of 
the causes. For example, in case of the group in 
the upper left-hand corner, the actual frequency is 
30,142, the theoretical frequency given by independ- 
ent probability is 28,360 ; the relative deviation 

is therefore ^ — = + .0628. For the sub- 

28360 

group in the upper right-hand corner the relative 

deviation is ^-^^-- = - .5599. In the first 

2988 

case, that is to say, in case of strikes for an increase 
of wages, there is a positive deviation of the success- 
ful strikes equal to 6.28 per cent, while in case of 
sympathetic strikes, there is a negative deviation 
of 55.99 per cent. 



124 



Laws of Wages 



TABLE VI. — The Rank of Causes of Strikes according as 
Strikes undertaken for the Particular Causes devi- 
ated, IN their Outcome, from Independent Probability 



Succeeded 


Succeeded Partly 


Failed 


(1) Concerning recog- 


(1) For increase of 


(1) In sympathy 


nition of the union 


wages. 


with strikers 


and union rules. 




elsewhere. 


(2) For reduction of 


(2) Against increase 


(2) Concerning em- 


hours. 


of hours. 


ployment of cer- 
tain persons. 


(3) Against increase 


(3) Against reduction 


(3) Concerning 


of hours. 


of wages. 


working rules 
and conditions. 


(4) For increase of 


(4) For reduction of 


(4) Against reduc- 


wages. 


hours. 


tion of wages. 


(5) Concerning work- 


(5) Concerning work- 


(5) Concerning rec- 


ing conditions and 


ing conditions and 


ognition of union 


rules. 


rules. 


and union rules. 


(6) Against reduction 


(6) In sympathy with 


(6) For reduction 


of wages. 


strikers elsewhere. 


of hours. 


(7) Concerning em- 


(7) Concerning em- 


(7) Against increase 


ployment of cer- 


ployment of cer- 


of hours. 


tain persons. 


tain persons. 




(8) In sympathy with 


(8) Concerning recog- 


(8) For increase of 


strikers elsewhere. 


nition of union 
and union rules. 


wages. 



In Table VI, the causes of strikes are ranked 
according as strikes undertaken for the particular 
causes deviate, in their outcome, from independent 
probability. It is found, for instance, that a strike 
for the recognition of the union has been the most 
likely to succeed ; a strike for an increase of wages 
has been the most likely to be compromised ; and 
a strike in sympathy with workers elsewhere has 



Wages and Strikes 



125 



been the most likely to fail. The other causes rank 
in the order of their sequence in the table. 

An examination of Table V also discloses that, 
during the period covered by the Report, the most 
important causes of strikes were " For an increase 
of wages " and " Concerning recognition of the union 
and union rules." These two causes of strikes, to 
which were due more than 50 per cent of all the 
strikes that occurred between 1881 and 1905, will 
be subjected to further treatment. 

TABLE VII. — Percentages of Total Strikes that were 

CALLED, respectively, FOR AN INCREASE OF WaGES AND 

FOR THE Recognition of the Union and Union Rules 



Tear 


For AN 

Increase of 
Wages 


Concerning 
THE Kecogni- 
tion of the 
Union and 
Union Eules 


Year 


For an 

Increase op 

Wages 


Concerning 
THE Recogni- 
tion of the 
Union and 
Union Eulbs 


1881 


61.15 


5.73 


1894 


30.54 


12.45 


1882 


54.41 


5.95 


1895 


41.98 


12.35 


1883 


45.40 


7.53 


1896 


26.80 


21.93 


1884 


29.57 


6.77 


1897 


35.81 


12.99 


1885 


37.52 


7.44 


1898 


36.36 


15.72 


1886 


41.69 


8.73 


1899 


38.84 


19.53 


1887 


33.64 


15.60 


1900 


32.94 


15.35 


1888 


2.5.94 


13.69 


1901 


29.04 


27.98 


1889 


29.95 


12.65 


1902- 


32.86 


25.27 


1890 


31.48 


12.88 


1903 


31.57 


23.24 


1891 


26.67 


14.27 


1904 


23.19 


32.42 


1892 


29.12 


15.25 


1905 


28.07 


30.86 


1893 


24.21 


13.72 









Table VII, which was taken from the volume on 
Strikes and Lockouts, 1906, p. 56, gives the per- 
centages of total strikes that were undertaken for 



126 



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Wages and Strikes 127 

these two causes between the years 1881-1905, in- 
clusively. When these figures are plotted, as in 
Figure 16, it is observed that the general trend of 
the percentage of strikes undertaken for an increase 
of wages has been downward, while the general 
trend of the percentage of strikes for a recognition 
of the union rules has been upward. Furthermore, 
there is an inverse correlation between the deviations 
in the tv/o cases, that is to say, when the percentage 
of strikes for an increase of wages rises above the 
general trend, the percentage of strikes for a recog- 
nition of the union tends to fall below the general 
trend and vice versa. The coefficient of correlation 
between these deviations from the general trend is^ 
7- =-.228. 

An additional light upon this very same question 
of the relation of these two causes is afforded by 
Table VIII, which is taken from the same Report 
on Strikes and Lockouts, p. 622. The table gives 
the percentages of total strikes that were successful 
when the causes of the strikes were, respectively, 
for an increase of wages and for a recognition of 
the union. The general trend — Figure 17 — of the 
percentages of total strikes that were successful was 
downward, in case of strikes for an increase of wages, 

1 No argument is dependent upon the absolute value of this 
coefficient. It contains a spurious element. 

The equation to the general trend, for the percentages of total 
strikes that were called for an increase of wages, is 7/ = 34.4:3 — .6466 x ; 
and for the percentages called for a recognition of the union, 
^ = 15. .57 + .8967 x, the origin in both cases being in the middle of the 
year 1893. 



128 



Laws of Wages 









Is «M 



R § ^ § ^ 



Wages and Strikes 



129 



and upward, in case of strikes for a recognition 
of the union. Moreover, the percentage deviations 
from the general trend ^ in case of successful strikes 
for the recognition of the union were inversely corre- 
lated with the percentage deviations from the gen- 
eral trend in case of successful strikes for an increase 
of wages. The coefficient of correlation is r= — .207. 

TABLE VIII. — Percentage op Strikes that were success- 
ful WHEN THE Causes of the Strikes were, respectively, 
FOR AN Increase of Wages and concerning the Recog- 
nition OF THE Union and Union Rules 



Year 


For an 

Increase op 

Wages 


Concerning 
THE Recogni- 
tion OP THE 

Union and 
Union Rules 


Yeak 


For an 

Increase op 

Wages 


Concerning 
the Recogni- 
tion OF THE 

Union and 
Union Rules 


1881 


73.62 


40.74 


1894 


31.04 


75.84 


1882 


56.86 


50.00 


1895 


37.11 


74.19 


1883 


74.31 


17.50 


1896 


62.15 


68.78 


1884 


57.25 


30.00 


1897 


40.92 


92.17 


1885 


61.13 


50.75 


1898 


60.60 


87.67 


1886 


66.44 


40.58 


1899 


53.06 


62.43 


1887 


48.97 


53.41 


1900 


37.60 


31.66 


1888 


63.53 


47.64 


1901 


53.92 


57.26 


1889 


53.45 


46.85 


1902 


56.29 


55.14 


1890 


45.64 


45.25 


1903 


46.98 


66.48 


1891 


37.01 


69.46 


1904 


39.22 


36.60 


1892 


55.01 


13.09 


1905 


45.73 


43.83 


1893 


47.39 


82.01 









Thus far it has been possible to establish that 
strikes for an increase of wages decreased in relative 

1 The equation to the general trend of the successful strikes for an 
increase of wages is ?/ = .52.45-.8614x; and for the recognition of the 
union, 2/ = 53.55+ .9848 x, the origin in both cases being in the middle 
of the year 1893. 



130 Laws of Wages 

importance in the interval 1881-1905; that the per- 
centage of successful strikes for an increase of wages 
decreased during the same period ; that during the 
same epoch there was an increase in the relative 
number of strikes for the recognition of the union and 
an increase in the percentage of successful strikes for 
the recognition of the union. Furthermore, it has 
been established that the percentage deviations from 
the general trend are inversely correlated both in case 
of the relative importance of the two causes of strikes 
and in case of the percentage of successful strikes due 
to the two causes. 

In view of the dominant importance of these two 
causes of strikes and of their interrelation, it is clear 
that if the outcome of strikes for either cause could 
be shown to be dependent upon economic law, a large 
part of the theory of strikes would be brought into 
intimate and real relation with the general theory of 
distribution. 

Table IX has been compiled from the data contained 
in M. Francois Simiand's work : Le Salaire des oimriers 
dee mines de charbon en France. On pages 351-365 
of that work M. Simiand has given the results of 
strikes relative to wages and conditions of work in 
the coal mining districts of the basins of Loire, Nord, 
and Pas-de- Calais. I have computed, for these three 
districts, in Chapter III, on '^ Wages and the Produc- 
tivity of Labor," the equation to the general trend of 
the ratio of wages to the value of the product per 
laborer per day, and I have given the percentage 



Wages and Strikes 



131 



deviations of these ratios, for eacli year, from the gen- 
eral trend, during the period 1848-1901. By means 
of these two bodies of results Table IX has been con- 
structed. The 112 strikes recorded by M. Simiand 
have been classified according as they fall into the 
sixteen subcontingency groups of the table. 

TABLE IX. — Contingency between the Rate of Wages 
AND THE Outcome of Strikes 







Pekoentage Deviation of Wages from 
THE General Trend 


Total 




Above +4 


to +4 


to -4 


Below — 4 


s 

W 
E-i 

O 

H 
O 

o 
f 
u 
O 


Successful 


3 


5 


12 


7 


27 


Very Favorably 
and Favorably 
Compromised 




1 


5 


1 


7 


Compromised 


6 


1 


11 


2 


20 


Failed 


18 


10 


26 


4 


58 


Total 


27 


17 


54 


14 


112 



When the coefficients of contingency are computed, 
it is found that (7i = .327 and C.2= between .36 and 
.37. The conclusions are — 

(1) The outcome of strikes for the causes affect- 
ing wages or the conditions of work is 



132 Laws of Wages 

related to the deviations from the general 
trend of the ratio of wages to the value 
of the product, that is to say, the outcome of 
strikes affecting wages and the conditions of 
work is likely to be favorable or unfavorable 
to the interests of the laborers according as 
the prevailing share of the laborer in the value 
of the product is below or above the general 
trend of that share ; 
(2) The measure of this relation is (7i=.327; 
C,= M-.S7. 

But the above coefficients relate to M. Simiand's 
entire number of strikes between the years 1848-1901. 
The causes of the tabulated strikes were, however, 
mixed causes. M. Simiand has included all causes 
affecting wages and conditions of work, and conse- 
quently such causes find their place in his table as 
payment for supplies, hours of work, employment of 
foreigners, conduct of overseers, and dismissal of work- 
men. But we have established that the outcome of 
strikes varies according to the causes of strikes, and 
therefore it is desirable to narrow the investigation 
and to inquire whether there is any relation between 
the rate of wages and the outcome of strikes for an 
increase of wages. 

Table X has been compiled from M. Simiand's data 
by including only those strikes that had their origin 
in a demand for an increase of wages. The material 
has been treated by the Pearsonian method for evalu- 



Wages and Strikes 



133 



ating the correlation ratio when one variable is given 
by alternative categories and the other by multiple 
categories. The percentage deviations from the gen- 
eral trend of the ratio of wages to the value of the 
product per laborer have been assumed to conform to 
the normal law. 



TABLE X. — Correlation between the Rate of Wages and 
THE Outcome of Strikes for an Increase of Wages 







Outcome of Strikes 


Total 




Succeeded 


Succeeded 
Partly 


Failed 


a 


Above general trend 


3 


1 


10 


14 


Below general trend 


8 


6 


11 


25 


Total 


11 


7 


21 


39 



The value of the correlation ratio is 17 = .370, which 
is the highest degree of relation that we have found 
in this chapter. The conclusions are (1) that the out- 
come of strikes for an increase of wages is related to 
the deviations from the general trend of the ratio of 
wages to the value of the product per laborer ; (2) the 
degree of the relation is measured by 17 = .370. The 
outcome of a strike for an increase of wages is likely 
to be favorable to the interests of the laborers when 
the ratio of wages to the value of the product per 
laborer is below the general trend of that ratio. The 
outcome is likely to be adverse to the interests of the 
laborers when the prevailing ratio is above the general 



134 Laws of Wages 

trend. The general trend itself, as we discovered in 
the chapter on " Wages and the Productivity of 
Labor," is conditioned by the degree and nature of the 
organization of capital and labor in production. 

Summary. 

In beginning this chapter it was assumed that both 
labor organizations and economic law affect the out- 
come of trade disputes as to wages, and the scientific 
task that was imposed was to measure, as far as 
possible with available data, the relative importance 
of the two factors in the determination of the result- 
ing rate of wages. The conclusions of the investiga- 
tion may be summarized under two headings ; {A) 
The influence of labor organizations ; {B) The 
influence of economic law. 

{A) The influence of labor organizations. 

(1) The results of strikes ordered by labor 

organizations are more favorable to the 
interests of the laborers than the results of 
strikes that are not ordered by labor or- 
ganizations. The measure of association 
between the outcome of strikes and the 
calling or not calling of strikes by labor 
organizations is given by 17 = .218. 

(2) The greater the degree in which labor organ- 

izations control the trade disputes of an 
industry, the more likely is the outcome of 
a strike declared by labor organizations to 
be favorable to the interests of laborers. 



Wages and Strikes 135 

The measure of association between the 
degree in which labor organizations control 
trade disputes and the outcome of strikes 
declared by labor organizations is given bj 
(7i = .232. 
(3) The greater the duration of a strike, the less 
likely is its outcome to be favorable to the 
interests of the laborers. The measure of 
association between the duration of strikes 
and the nature of the outcome of strikes is 
(7i = .22 in case of Germany, and (7^ = .16 
in case of France. 
(B) The influence of economic law. 

The relations summarized under (A) must not be 
assumed to be relations of cause and effect. 
The low coefficients measuring the degrees 
of association preclude any inference as to 
causal relations. Moreover, the results are 
aggregate results of mixed causes and mixed 
conditions. A complete investigation would 
require a segregation of the material and its 
treatment according to differing conditions 
and causes. The results of this preliminary 
study, which goes as far in the direction of seg- 
regation of materials as the present sources 
will admit, are as follows : — 
(1) The outcome of strikes is associated with the 
kinds of causes for which strikes are un- 
dertaken. The coefficient measuring the 
degree of association is (7i = .298. 



136 Laws of Wages 

(2) The causes of strikes may be ranked accord- 

ing as they have been the origin of strikes 
that succeeded, succeeded partly, or failed. 

(3) The most important causes of strikes have 

. been " for an increase of wages " and " for 
the recognition of the union and union 
rules." 

(a) The general trend of the ratio of strikes 
"for an increase of wages" to total 
strikes has been downward ; the gen- 
eral trend of the ratio of strikes " for 
the recognition of the union" to total 
strikes has been upward. 

(6) The general trend of the ratio of success- 
ful strikes " for an increase of wages" 
to total strikes " for an increase of 
wages" has been downward; the gen- 
eral trend of the ratio of successful 
strikes " for the recognition of the 
union" to total strikes "for the 
recognition of the union" has been 
upward. 

(c) There is an inverse correlation between 
the percentage deviations from the 
general trend of the ratio of strikes 
"for an increase of wages" to total 
strikes, and the percentage deviations 
from the general trend of the ratio 
of strikes " for the recognition of 
the union " to total strikes. 



Wages and Strikes 137 

(d) There is an inverse correlation between 
the percentage deviations from the 
general trend of the ratio of successful 
strikes "for an increase of wages" to 
total strikes "for an increase of wages," 
and the percentage deviations from 
the general trend of the ratio of suc- 
cessful strikes " for the recognition of 
the union" to the total strikes "for 
the recognition of the union." 
This intimate connection of the two most 
important causes of strikes led to the 
attempt to connect one of the causes 
with the economic laws that have 
been established in a preceding chap- 
ter. It was found that — 
(4) The results of strikes for general causes 
affecting wages and conditions of work 
are associated with the percentage devia- 
tions of the laborer's share of the product 
from the general trend of that share. The 
outcome of a strike for general causes 
affecting wages and conditions of work 
is likely to be favorable to the interests 
of the laborers when the laborer's share in 
the product of industry is below the gen- 
eral trend of that share. The outcome 
of the strike is likely to be adverse to 
the interests of the laborers when the 
laborer's share is above the general trend. 



138 Laws of Wages 

The coefficient measuring the association 
is Ci = .327. 
(5) The outcome of a strike " for an increase of 
wages " is related to the percentage devia- 
tion of the laborer's share of the product 
from the general trend of that share. The 
result is likely to be favorable if the la- 
borer's share is belovv^ the general trend ; it 
is likely to be adverse, in the contrary case. 
The measure of the relation is 77 = .370. 
This last coefficient is based upon a small num- 
ber of cases and consequently the probable 
error is high. From the nature of the data 
examined there is reason for supposing 
that, with a larger number of cases, the 
correlation ratio would be much higher. 



CHAPTER VI 

WAGES AND THE CONCENTRATION OF INDUSTRY 

" II mettere in luce 1' influenza dell' impresa e dell' eta dell' operaia 
suir altezza dei salari, ci sembra ricerca della maggiore importauza 
teorica e pratica." 

— La Donna Nell' Industria Italiana, p. ix. 

The investigation upon which we are about to enter 
as to the influence upon the status of the laborer of 
the concentration of industry in large establishments 
is of both theoretical and practical importance. Its 
practical value lies in the answer to the question as 
to whether the form of selection of laborers entailed 
by the survival in competition of large establishments 
places the employees upon a better plane of living 
than the one occupied by their fellow-workers in 
smaller establishments. Its theoretical interest lies 
in the answer to the query as to whether the pro- 
ductivity hypothesis will explain the results to which 
the investigation will lead. 

We shall approach our problem by considering the 
relation of the size of the establishment (1) to the 
rate of wages, (2) to the amount of employment, 
(3) to the continuity of employment, and (4) to the 
length of the working day. 

Because of the complexity of the undertaking, 
there is great likelihood of obtaining spurious re- 

139 



140 Laws of Wages 

suits in consequence of the mixing of heterogeneous 
data. The following cautions should be observed as 
far as possible in selecting material upon which to 
base the investigation : Data should be segregated 
(1) referring to different sexes; (2) referring to la- 
borers of different ages ; (3) according as the data are 
drawn from different geographical districts ; (4) ac- 
cording as they are drawn from city and country; 
(5) referring to industries bearing the same generic 
name but producing different commodities. Unfor- 
tunately, statistics appropriate to the solution of dif- 
ficult economic problems cannot be had for the ask- 
ing, so that, in the treatment of several points in this 
chapter, I have been compelled to use data that do 
not in all respects fulfill ideal requirements. 

Wages as Affected hy the Concentration of Industry. 

The first three tables in the Appendix to this chap- 
ter refer to the daily wages of women, above fifteen 
years of age, employed in the manufacture of textiles 
in Italy. ^ 

We obtain, 

(1) from Table I, the coefficient of mean square 
contingency between the size of the estab- 
lishment and the rate of wages, 

Ci=.318; 

^ The tables in this chaptei' that present Italian data are drawn 
from the publication of the Ufficio del Lavoro : La Donna Nell' Indus- 
tria Italiana, Roma, 1905. 



Wages and the Concentration of Industry 141 

(2) from Table II, the coefficient of mean square 

contingency between the rate of wages and 
the age of the worker, 

C,= M; 

(3) from Table III, the coefficient of mean square 

contingency between the age of the laborer 
and the size of the establishment, 

C, = M. 

With these crude coefficients of contingency, it 
would be possible to evaluate, by the method of mul- 
tiple contingency, the net relation between wages 
and the size of the establishment. But such a net 
coefficient would not be an adequate index of the 
real connection between the phenomena. The de- 
tails of the computation of the above coefficients 
have made it abundantly clear that the interrela- 
tions between the size of the establishment, the rate 
of wages and the age of the laborer cannot be suffi- 
ciently described by the simple linear laws that are 
obtained in the usual cases of correlation. 

Let us first endeavor to find the law of the varia- 
tion of wao;es with the a^re of the laborer. 

Tables I and II of the text have been computed 
from Table IV of the Appendix. ^ Knowing the 
mean ages of the laborers in the separate wage groups 
and the mean wages earned by laborers in the same 

1 Table IV of the Appendix was copied from the publication, La 
Donna NelV Industria Italiana, pp. 99-100. 



142 



Laws of Wages 



TABLE I. — Mean Daily Wages of Italian Women accord- 
ing TO THEIR Ages and the Sizes of the Establishments in 

WHICH they were AT WORK 



Age of 
Employees 


Mean Daily Wages received in Establishments with 


Less than 20 
Employees 


20-99 


100-499 


500 and Over 


15-20 


.87 


.93 


1.04 


1.24 


20-35 


1.09 


1.10 


1.21 


1.50 


35-55 


1.05 


1.12 


1.17 


1.48 


Above 55 


.92 


.98 


.98 


1.16 



TABLE II. — Mean Ages of the Employees in the Several 
Age Groups of the Four Classes of Establishments. 
Textiles. Italy. 



Size op 
Establishment 


Age Groups 


Above 15 


15-20 


20-;35 


85-55 


Above 55 


Less than 20 
employees 


28.23 


17.32 


25.82 


44.43 


58.20 


20-99 


25.63 


17.30 


25.33 


44.72 


57.53 


100-499 


25.14 


17.30 


25.22 


44.89 


57.58 


500 and Over 


24.32 


17.31 


25.34 


43.63 


57.49 



groups, we can deduce the approximate law of the 
variation of wages with the age of the laborer. Fig- 
ure 18 is the graphical description of the variation of 
wages with the age of the female workers, above 



Wages and the Concentration of Industry 143 

fifteen years of age, engaged in the manufacture of 
textiles in Italy. The four curves upon the chart 
give the variation of wages with the age of the la- 
borer, for the establishments of different sizes. 

The curves show : — • 

(1) That the law of the variation of wages with 

the age of the laborer is, in general charac- 
ter, the same in establishments of different 
sizes : There is a rapid rise of wages to a 
maximum, between twenty-five and thirty- 
five years of age, and a slow descent to old 
age. 

(2) That the larger the establishment the higher 

the wages at all ages. (This may be partly 
due to the fact that data from the whole of 
Italy were mixed in the summary table that 
has been used.) 

(3) That in case of the smaller establishments — 

establishments "less than 20 employees," 
and between "20 and 99 employees" — the 
wages of the old employees are higher than 
the wages of the young employees, while 
the contrary is true of the larger establish- 
ments. (Compare the columns in Table I 
of the text.) 

(4) That the descent from the maximum wage is 

more rapid in the large establishments.^ 
(Compare the curves in Figure 18.) 

^ The above method and conclusions are submitted as contribu- 
tions to Professor Max Weber's problem : " Es ist eine der wichtig- 



144 



Laws of Wages 




&l/// a/pasffSJc/)£0 S'aiS&y///ec7 



Wages and the Concentration of Industry 145 

Why should the law of the variation of wages 
with age take this peculiar form ? Why should there 
be a rapid rise to a maximum between twenty-five 
and thirty-five years of age and a slow descent to old 
age ? And why should the graphs descriptive of the 
operation of the law in the four classes of estab- 
lishments be disposed in the same order as the sizes 
of the establishments ? The productivity hypothesis 
supplies the proper answer to all of these questions. 

We shall consider first the bearing of the produc- 
tivity hypothesis upon the shape of the age-wage 
curve. In Chapter IV we found that the efficiency 
of the laborer is dependent upon a balance of physi- 
cal, mental, and moral qualities, and that the wage of 
the laborer is dependent upon his industrial efficiency. 
In the present chapter we have discovered the law of 
the variation of wages with the age of the laborer. 
If the productivity hypothesis be the true explanation 
of wages, it would follow that the efficiency of the 
laborer — his balance of physical, mental, and moral 
qualities — must vary with age in a manner similar 



sten Aufgaben, fiir die einzelnen Industrien, innerhalb ihrer die ein- 
zelnen Arbeiterkategorien und fiir diese wieder nach den einzelnen 
ethnischen, sozialen iind Berufs-Provenienzen festzustellen : wie 
schnell oder langsara sie ein solches Mass von Leistungsfiihigkeit 
erlangen, dass ihre Verwendung als Vollarbeiter rentabel wird, wann 
sie den Hohepunkt ihrer Leistung erreichen, wie lange sie sicb auf 
dieser Hohe behaupten und -wann ihre Leistungsfahigkeit so weit 
sinkt, dass sie nicht mehr als Vollarbeiter, oder schliesslich iiberhaupt 
nicht mehr fiir die betreffende Arbeitsart verwendbar sind." " Zur 
Psychophysik der industriellen Arbeit," Archiv fiir Sozialwissenschaft 
unci Sozialpolitik, 1909, pp. 270-271. 



146 Laws of Wages 

to the variation of wages with age : it must rise 
rapidly to a maximum between twenty-five and 
thirty-five years of age and then descend slowly to 
old age. There can be very little doubt, I think, that 
among the mass of laborers industrial efficiency varies 
with age according to this law. The study of certain 
physical measurements is confirmatory of this belief. 
In a paper by A. 0. Powys on " Data for the Prob- 
lem of the Evolution in Man," ^ the following im- 
portant truths are discovered : — 

(1) The law of the variation of stature with age, 

in case of the experience of New South 
Wales, is that stature increases rapidly from 
the age of fifteen to a maximum between 
twenty-five and thirty years of age and then 
decreases slowly to old age. (The maxi- 
mum stature of men is reached at about 
twenty-eight years of age and of women at 
about twenty-five.) 

(2) " The modal fertility of Victorian women is at 

27 and of Victorian men at 32. For New 
South Wales women the modal fertility 24.4, 
two to three years less than for Victoria. 
We have not the data for New South Wales 
men, but they would probably show a mode 
of about 29-30 instead of 32. Thus we see 
that the age of maximum fertility at any 
rate approaches, if it does not coincide with, 
the age of most fully developed stature. As 

1 Biometrika, Vol. I, pp. 30-49. 



Wages and the Concentration of Industry 147 

Mr. Powys remarks, this tendency of maxi- 
mum stature age to coincide witli that of 
maximum fertility can hardly be fortuitous. 
It seems probable that in man, as in other 
types of life, the age of maximum fertility 
is the age of most fully developed physique." ^ 

The law of the variation of wages with age is 
therefore similar to the law of the development of 
physique, and both fertility and industrial efficiency 
reach their maxima, in the mass of laborers, at about 
the period of most fully developed physique. This 
resemblance in the general character of the law of 
the development of physique and the law of the vari- 
ation of wages with age, together with the approxi- 
mate coincidence of the periods of fully developed 
physique, maximum fertility, and maximum industrial 
efficiency leaves very little room for doubt as to the 
intimate causal relation of the phenomena. The facts 
are all in harmony with the a priori doctrine that 
the laborer's income is dependent upon his efficiency, 
and that consequently the law of the variation of his 
income is similar to the law of the variation of his 
efficiency. 

We may now consider the manner in which the 
productivity hypothesis supplies the answer to the 
question as to why the graphs descriptive of the varia- 
tion of wages with the age of the laborer are disposed 

^ Remarks of Professor Pearson upon Mr. Powys' data, Biometrika, 
Vol. I, p. 48. 



148 Laws of Wages 

upon the chart in the same order as the sizes of the 
establishments. 

Two points may be made : — 

(1) The large establishments select the more effi- 

cient laborers. Referring to the payment of 
higher wages in large establishments, the 
French report Salaires et duree du travail 
dans V Industrie fran^aise makes the following 
observation : — 

" Cette tendance ne se manif este pas senlement en faveur 
des industries qui, comme les mines, les usines 
metalkirgiques, les compagnies de transiDort, sont le 
terrain propre de la grande industrie : on Vohserve 
encore dans (Vautres groupes ou les grands etablisse- 
ments compensent, par des avantages economiqties 
certains, la contrainte morale que la concentration des 
entreprises impose d la ptopidation ouvrih'e, laquelle ne 
renonce pas sans regret ci la vie plus irregulih'e, mais 
en un sensjjlus independante, de Vancienne industries ^ 

(2) Because of the use of large fixed capital in 

large establishments, the more efficient 
workers are more valuable to the large than 
to the small establishments. 

'^ We have hitherto supposed that it is a matter of in- 
difference to the employer whether he employs few 
or many people to do a piece of work, provided his 
total wages-bill for the work is the same.' But that 
is not the case. Those workers who earn most in a 

^ Vol. IV, p. 22. I have italicized the part of the quotation that I 
wish to emphasize. 



Wages and the Concentration of Industry 149 

week when paid at a given rate for tlieir work are 
those who are cheapest to their employers (and 
ultimately to the community, unless indeed they 
overstrain themselves, and work themselves out pre- 
maturely). Yov they use only the same amount of 
fixed capital as their slower fellow workers; and, 
since they turn out more work, each part of it has to 
bear a less charge on this account. The prime costs 
are equal in the two cases ; but the total cost of that 
done by those who are more efficient, and get the 
higher time- wages, is lower than the total cost of 
that done by those who get the lower time-wages at 
the same rate of piece-work paj'^ment." " This point 
is seldom of much importance in out-of-door work, 
where there is abundance of room, and comparatively 
little use of expensive machinery ; for then, except 
in the matter of superintendence, it makes very 
little difference to the employer, whose wages-bill 
for a certain piece of work is £100, whether that 
sum is divided between twenty efficient or thirty 
inefficient workers. But when expensive machinery 
is used ivhich has to be loroportioned to the number of 
workers, the employer ivould often Jind the total cost of 
his goods lowered if he could get twenty men to turn 
out for a wages-bill of £ 50 as much work as he 
had previously got done by thirty men for a ivages-bill 
of £40.''^ 

We infer from the quoted facts that the higher 
wages paid in the larger establishments are due to 
the greater productivity of a personnel which, age for 
age, is superior in a balance of physical, mental, and 
moral qualities. 

1 Marshall: Principles of Economics, 4th edit., pp. 631-632. The 
part of the quotation that I wish to stress I have italicized. 



150 Laws of Wages 

The next detail to be examined is that of the dif- 
ferences in the age grouping of the operatives in large 
and in small establishments. The curves descriptive 
of the frequency distributions according to the age of 
the employees in establishments of different sizes may 
be deduced from Table IV of the Appendix. The 
method that I have adopted may be understood from 
the following illustration. Table IV gives the infor- 
mation that, in establishments employing at least 500 
women, 41.9 per cent of the employees were between 
15 and 20 years of age ; 47.3 per cent between 20 and 
35 ; 9.8 per cent between 35 and 55; and 1 per cent 
over 55. Assuming that no employee was over 65 years 
of age, the preceding age distribution may be expressed 
in cumulative form as follows : 100 per cent were 
over 15 years of age ; 58.1 per cent over 20 years of 
age ; 10.8 per cent over 35 ; 1 per cent over 55 ; and 
zero over 65. By fitting a parabola of the fourth 
order to the age distribution in the cumulative form, 
the equation to the age distribution is found to be 

y = 7.167674 - .518268 x + .028171 x' - .0023708 x^ 
+ .000064577 x\ 

where, the origin being taken at 40, (40 + x) repre- 
sents the age and y the cumulative percentage 
frequency. By differentiating the equation and 
changing the signs of the quantities, the frequency 
distribution according to age is obtained in the usual 
form. The equation in the differential form is 

y = .518268 - .056342 x + .00711 24 x' - .0002583 x\ 



Wages and the Concentration of Industry 151 

From this latter equation, since the origin is at 40, 
the mean of the distribution may be found from 

/a 
yxdx 



40 + 



£yd^. 



and the standard deviation of the 



distribution from 



I yx'-dx r / yxd. 

tlA Jb 



j ydQ 



ydx 



Inas- 



much as the lower age limit in the four groups 
of establishments is 15 years of age, h, the lower 
limit of integration, is - 25. The upper limit of inte- 
gration, a, is determined by the point where the 
curve cuts the axis of x and is different in the four 
types of establishments. 

By utilizing this method, Table III of the text is 
derived. 



TABLE III. — Means and Standard Deviations op the Ages 
OF Employees, according to the Sizes of the Establish- 
ments 





Size op Establishments 


Below 20 
Employees 


20-99 


100-499 


500 and 
Over 


Mean Age 


28.23 


2.5.63 


25.14 


24.32 


Standard Deviation . . . 


12.25 


10.84 


10.59 


9.37 



We see from this table that — 
(1) the larger the establishment, the lower is the 
mean age of the employees ; 



152 



Laws of Wages 













































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CJ <0 N to lO th <>> 



Wages and the Concentration of Industry 153 

(2) the larger the establishment, the smaller is the 
" scatter " about the mean age. 

It follows from these two facts that the bulk of 
the adult personnel in the four classes of establish- 
ments is younger, the larger the establishments. 

In Figure 19 the percentage distribution of the 
operatives in the four classes of establishments is 
roughly indicated by a series of broken lines. The 
most marked feature of the graphs is that above 
forty years of age the percentage frequencies are in 
inverse order of the sizes of the establishments — the 
smaller establishments having at all ages above 40 a 
larger percentage of workwomen than the large 
establishments. 

Amount of Employment. 

We come now to the consideration of the relation 
of the size of the establishment in which laborers are 
at work to the amount of employment afforded 
by the establishments in the course of the year. 
We shall seek to know whether the mean num- 
ber of days in which the laborers are employed 
in a year bears any relation to the size of the estab- 
lishment in which they are at work. The material 
used in the investigation is again drawn from the 
admirable report, La Donna NelV Industria Italiana. 

In the Appendix, Table V, which was compiled 
from the Italian report, summarizes the data relating 
to the manufacture of textiles. From this Table V 
two contingency tables — Tables IV and V of the 



154 



Laws of Wages 



TABLE IV. — Contingency between the Amount of Employ- 
ment AND THE Size of Establishments. Textiles. La 
Donna Nell' Industria Italiana. 



Mean Number 

OF Days, pek 

Establishment, 

worked in 

A Year 


Number of Women in Establishments 
OF Sizes given Below 


Total 


Less 
than 20 


20-99 


100-499 


500 and 
Over 


245-255 


1167 


25,007 






26,174 


255-265 






62,930 




62,930 


265-275 


999 






6789 


7788 


275-285 




3772 






3772 


285-295 




3744 


25,700 




29,444 


295-305 






4936 


16,269 


21,205 


Total 


2166 


32,523 


93,566 


23,058 


151,313 



text — have been constructed. Both of the contin- 
gency tables refer to the relation of the amount of 
employment to the size of the establishment, but 
they differ in respect to the system of weighting the 
amount of employment. The original Italian report ^ 
gives the number of establishments of various sizes, 
the mean number of days, per establishment, worked 
during the year by the establishments of the several 
sizes, and the total number of workwomen over fifteen 

1 Pages 54-62. 



Wages and the Concentration of Industry 155 

TABLE V. — Contingency between the Amount of Employ- 
ment AND the Size of Establishments. Textiles. La 
Donna Nell' Ixdustria Italiana. 



Mean Numbek 
OF Dats, per 

ESTABLISHME^fT, 

worked in a 
Yeae 


Number of Establishments of Sizes given Below 


Total 


Less than 20 
Employees 


20-99 


100-499 


500 and 
Over 


24.5-255 


116 


613 






729 


255-265 






462 




462 


265-275 


123 






11 


134 


275-285 




92 






92 


285-295 




99 


130 




229 


29.5-305 






27 


26 


53 


Total 


239 


804 


619 


37 


1699 



years of age employed in the establishments of the 
several classes, on the 30th of November, 1903. 

In the contingency Table IV, the mean number of 
days worked in a year, per establishment, is weighted 
in each case, with the number of workwomen em- 
ployed in the establishments of the class in question, 
on the 30th of November, 1903. For example, 1167 
women over 15 years of age were employed, on the 
30th of November, 1903, in establishments in which 
the mean number of days' work, per establishment, in 
the preceding year, was between 245 and 255. 



156 Laws of Wages 

In the contingency Table V, the mean number of 
days worked in a year, per establishment, is weighted 
in each case with the number of establishments of 
the various sizes falling within the limits of the par- 
ticular "days worked" group. For example, 116 
establishments employing less than 20 women each 
worked on the average between 245-255 days, in the 
year from December 1, 1902, to November 30, 1903. 

When the coefficients of contingency are calculated 
in the usual way from these two tables, we find that — 

(1) in the first system of weighting, Table IV, 

Ci = .791; (7,= .89; 

(2) in the second system of weighting. Table V, 

(7i=.785; Co = .88. 

These very high coefficients are marked indications 
of the gains to laborers, in the way of amount of em- 
ployment, that accrue in consequence of the superior 
management necessitated by the investment of vast 
capital in enterprises producing upon a large scale. 

Continuity of Employment. 

The third aspect of our problem as to the relation 
of the status of the laborer to the size of the estab- 
lishment in which he is employed is concerned with 
the variability of the amount of employment in course 
of the year. It has just been proved that the larger 
the establishment, the greater the amount of annual 
employment. We now inquire as to whether the 



Wages and the Concentration of Industry 157 

amount of employment afforded by the establish- 
ments of the various sizes is more or less variable, 
from month to month, in the larger establishments 
than in those of the smaller types. 

Table VI of the text, referring to the manufacture 
of textiles in Italy, was summarized from the report 
that has proved so valuable in the other investiga- 
tions of this chapter. It gives, for establishments of 
various sizes, the monthly indices of employment, in 
the more important subdivisions of the textile indus- 
try, together with the minimum, mean, and maxi- 
mum monthly variations, in the year December 1, 
1902, to November 30, 1903. 

The method of presenting these results is due to 
Professor Bagni,^ who had charge of the preparation 
of the report. La Donna NelV Industria Italiana. 
Before commenting upon the data of Table VI, we 
shall consider the method of computing the monthly 
indices of employment. 

For every establishment investigated, the Italian 
Bureau of Labor had data showing, for each month 
in the year December 1, 1902, to November 30, 1903, 
the number of days in which the establishment was 
in operation and the mean daily number of work- 
women who were employed. It was, therefore, pos- 
sible to compute for each class of estabhshments 
the total number of workwomen-days-work in each 
month. For, obviously, the number of workwomen- 
days-work in establishment X diu-ing the month T 

1 La Donna Nell' Industria Italiana, p. ix. 



158 



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Wages and the Concentration of Industry 159 



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160 Laivs of Wages 

was equal to the number of days the establishment 
was in operation multiphed by the average daily 
number of workwomen employed that month. By 
means of this method the number of workwornen- 
days-work in each of the four groups of establish- 
ments was computed for each month of the year 
and for the whole year. The monthly numbers were 
afterwards expressed as fractions of the correspond- 
ing annual numbers, and the fractions were then 
multiplied by 1200. The resulting numbers are Pro- 
fessor Bagni's monthly indices of employment. The 
maximum, mean, and minimum variations are meas- 
ured from 100.^ 

We may now examine Table VI. By referring to 
the last two columns we observe that — 

(1) As the size of the establishment increases, the 

general trend of the mean variations of the 
index of employment is downward. (The 
silk industry is an exception to the rule.) 

(2) As the size of the establishment increases, the 

general trend of the maximum deviation is 
downward. (The silk industry is again an 
exception to the rule.) 

(3) In all of the groups, the mean deviation and 

maxinmm deviation in the largest establish- 
ments are smaller than the corresponding 
deviations in the smallest establishments. 

^ The objection to this method is that spurious monthly diiierences 
are introduced in consequence of not taking into account the differ- 
ences in the length of the calendar months. The defect in the 
method does not invalidate the inferences in the text. 



Wages and the Concentration of Industry 161 

Length of the Working Day. 

The fourth aspect of the problem as to the relation 
of the status of the laborer to the size of the estab- 
lishment in which he is employed is concerned with 
the length of the working day. Up to this point the 
researches of this chapter have been based upon the 
data relating to the textile industry in Italy. It 
would be highly desirable to have all of our conclu- 
sions bearing upon the concentration of industry re- 
late to one industry at a given time and place. But 

TABLE VII. — Mean Duration of Daily Hours of Work, 

CONSIDERED IN RELATION TO THE SiZE OF ESTABLISHMENTS, 

IN THE Mines of France producing Coal and Other 
Fuel 



LOOALITT 


Mean Duration of Daily Hours of Work 
according as the establishment had a 
Number op "Workmen 


Exceeding 
999 


From 500 
to 999 


From 100 
to 499 


From 25 
to 99 


From 1 
to 24 


Region Nord et Pas-de- 
Calais 


8f 


9i 


H 






Region Est 


8f 




9 




101 


Region Centre .... 


9 


9J 


9i 


10 




Region Sud 


9i 


H 


10 






Region Sud-Est .... 




8i 


10 


H 




Region Bouches-du-Rhone 




8i 


8i 







162 Laws of Wages 

I do not know of the existence of material jjresenting 
a classification, according to sizes of establishments, 
of the hours of labor in the manufacture of textiles 
in Italy. 

In default of appropriate Italian figures, we may 
refer to the investigation embodied in the French 
report : Salaires et duree du travail dans V Industrie 
fpan<^aise. Table VIP is given as a favorable in- 
stance of the findings of the French statisticians. 
This table eliminates the differences in hours of 
labor arising from the differences in locality, and it 
clearly shows that as a general rule the hours of labor 
decrease as the size of the establishment increases. 

The conclusion that is drawn from this illustration 
is the conclusion of the French report as to the 
general trend in the whole of the French provincial 
manufactures. The conditions of production in Paris 
are exceptional, and statistical study of the relation 
of the size of the establishment to hours of labor is 
rendered difficult because of the classification under 
the same name of industries that are radically differ- 
ent in character. " En province, an contraire, les 
fabrications sont plus courantes, les divers etablisse- 
ments groupes sous le meme nom d'industrie forment 
des groupes plus homogenes. On pent meme les 
etudier, et on observe nettement une amelioration des 
conditions du travail dans les grandes entreprises. 
Dans leur ensemble, la duree du travail est plus 
courte."^ 

1 This table is taken from Vol. IV, p. 100. ^ /j/j.^ p, oo. 



Wages and the Concentration of Industry 163 

We started out to find the relation of the concen- 
tration of industry to the changing status of the 
laborer, and we proposed to investigate that relation 
from the four points of view of (1) the rate of wages, 
(2) the amount of employment, (3) the continuity of 
employment, and (4) the length of the working 
day. Our investigation has yielded the definite 
result that, as the size of the establishment increases, 
the condition of the laborer improves in all directions 
— his wages rise, he is employed a greater number of 
days in a year, his employment varies less from 
month to month, and his hours of labor, per day, 
-decrease. 

We have found that the law of the variation of 
wages with the age of the laborer is similar in estab- 
lishments of all sizes, and that the general character 
of the law has its explanation in the law of the de- 
veloping physique and capacity of the laborer. The 
differences in the graphs representative of the law of 
the variation of wages with the age of the laborer in 
the four types of establishments are due to the large 
establishments selecting the more capable workers. 
The large establishments are able to carry out the 
work of selection because, in consequence of their 
large capital and better organization, they offer op- 
portunities for the more capable laborers to reap the 
reward of their differential ability. 



164 



Laws of Wages 



APPENDIX 

TABLE I. — Contingency between the Daily Rate of Wages 
AND THE Size of the Establishment in which Employees 

WERE AT AVORK. TEXTILES. ItALY. 



Kate of 
Wages in 
Lire and 
Centesimi 


Number of Workwomen in KsxAULisuiiE^TS with 


Totals 


Less than 20 
Employees 


From 
20-99 


From 
100-499 


500 
and Over 


Up to .50 


150 


545 


1030 


96 


1821 


.51-.70 


443 


6303 


9356 


1103 


17,205 


.76-1.00 


873 


12,863 


30,523 


3718 


47,977 


1.01-1.50 


645 


11,239 


45,113 


10,605 


67,602 


1.51-2.00 


214 


1843 


7097 


6396 


15,550 


2.01-2.50 


30 


519 


1755 


1482 


3786 


Over 2.50 


6 


177 


613 


413 


1209 


Totals 


2361 


33,489 


95,487 


23,813 


155,150 



Wages and the Concentration of Industry 165 



TABLE II. — Contingency between the Daily Rate of Wages 
AND THE Age of the Laborer. Textiles. Italy. 



Rate of Wages 

IN 

Like and Centesimi 


Number op Employees whose Ages weke in the 
Age-gkoups 


Totals 


15-20 


20-35 


35-55 


Above 55 


Up to .50 


1425 


228 


105 


63 


1821 


.51-.75 


11,000 


4063 


1478 


664 


17,205 


.76-1.00 


21,903 


18,843 


6049 


1182 


47,977 


LOl-1.50 


24,905 


33,884 


8010 


803 


67,602 


1.51-2.00 


4184 


9103 


2109 


154 


15,550 


2.01-2.50 


555 


2511 


676 


44 


3786 


Above 2.50 


98 


807 


289 


15 


1209 


Totals 


64,070 


69,439 


18,716 


2925 


155,150 



166 



Laws of Wages 



TABLE ITT. — Contingency between the Age of Employees 
ANO THE Size of the Establishment in which they were 
AT Work. Textiles. Italy. 



AliK IN 

Ykaks 


NUMliEU OK WOKKWOMEN IN KslAUl.ISllMKNT8 W ITIl 


Totals 


Less than 20 
Employees 


20-99 


100-499 


500 and 
Over 


15-20 


778 


13,453 


39,851 


9988 


64,070 


20-35 


1005 


14,831 


42,367 


11,230 


69,439 


35-55 


471 


4543 


11,367 


2335 


18,716 


Over 55 


107 


602 


1902 


254 


2925 


Totals 


2361 


33,489 


95,487 


23,813 


155,150 



Wages and the Concentration of Industry 167 

TABLE IV. — Classification of Workwomen according to 
THEIR Ages, their Rates of Wages, and the Sizes of the 
Establishments in which they were employed. Textiles. 
La Donna Nell' Industria Italiana, pp. 99-100 



Size or the 

ESTABLISU- 

WENT8 


Percentage of Workwomen, over 15 Years of Age, 

RECEIVING THE FOLLOWING EaTE OF WaGES. 

[Kates are expressed in Centesimi and Lire] 


Age Groups 


Up to 
.50 


.51- 
.75 


.T6- 
1.00 


1.01- 
1.50 


1.51- 
2.00 


2.01- 
2.50 


Above 

2.50 


Total 
Per- 
centage 


Less than 

20 
Employees 


4.0 


8.5 


12.1 


7.0 


1.3 






32.9 


15-20 


1.3 


6.4 


15.0 


13.3 


5.4 


1.0 


.2 


46.6 


20-35 


.5 


3.0 


8.2 


6.0 


2.1 


.3 




20.1 


35-55 


.5 


.9 


1.7 


1.0 


.3 






4.4 


Above 55 


6.3 


18.8 


37.0 


27.3 


9.1 


1.3 


.2 


100.0 










20-99 


1.2 


11.1 


15.6 


11.2 


.9 


.2 




40.2 


15-20 


.2 


5.9 


16.5 


17.1 


3.3 


1.0 


.3 


44.3 


20-35 


.1 


1.6 


5.4 


4.8 


1.2 


.3 


.2 


13.6 


35-55 


.1 


.3 


.9 


.5 


.1 






1.9 


Above 55 


1.6 


18.9 


38.4 


33.6 


5.5 


1.5 


.5 


100.0 










100^99 


.9 


6.5 


14.9 


17.1 


2.0 


.2 


.1 


41.7 


15-20 


.1 


1.9 


12.4 


24.1 


4.3 


1.3 


.4 


44.5 


20-35 


.1 


.9 


3.9 


5.5 


1.0 


.3 


.2 


11.9 


35-55 




.5 


.8 


.5 


.1 






1.9 


Above 55 


1.1 


9.8 


32.0 


47.2 


7.4 


1.8 


.7 


100.0 










500 and 
Over 


.3 


3.7 


9.1 


19.5 


8.1 


1.1 


.1 


41.9 


15-20 


.1 


.6 


4.9 


20.5 


15.8 


4.1 


1.3 


47.3 


20-35 




.2 


1.3 


4.1 


2.9 


1.0 


.3 


9.8 


35-55 




.1 


.3 


.5 


.1 






1.0 


Above 55 


A 


4.6 


15.6 


44.6 


26.9 


6.2 


1.7 


100.0 





168 



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CHAPTER VII 

CONCLUSIONS 

" Womit wir es hier zu thun haben, ist eine kommunistische 

Gesellschaft, nicht wie sie sich auf ihrer eigenen Grundlage entwick- 

elt hat, sondern umgekehrt, wie sie eben aus der kapitalistischen 

Gesellschaft hervorgeht; die also in jeder Beziehung okonomisch, 

sittlich, geistig, noch behaftet ist mit den Muttermalen der alten 

Gesellschaft, aus deren Schoos sie herkommt." 

— Karl Marx. 

In the preceding chapters we have been concerned 
entirely with the scientific aspects of the subjects 
that came before us, and no attempt was made to 
indicate the practical bearing of the results that were 
established. But the economist, least of all scientists,\ 
can feel content with the simple understanding of ' 
the laws of his subject matter. He desires to see 
what guidance they may afford in the complicated 
life of his own time. This summary will, accord- 
ingly, be concerned primarily with the relation of our 
results to actual practice. 

We may notice first the practical character of Sta- 
tistical Economics. It was pointed out in the first 
chapter that in its scientific character, Statistical 
Economics proposes this twofold object : (1) to bring >^ 
to the test of representative facts the hypothe- 
ses and theorems of pure economics ; (2) to supply > 

169 



170 Laws of Wages 

data, in the form of general facts and empirical laws, 
for the elaboration of dynamic economics. Its prac- 
tical service is performed in a similar way ; for, in 
giving a statistical summary and interpretation of 
the material relevant to the economic subject under 
investigation, it supplies the means by which general 
reasoning may be brought to bear upon the problems 
of industrial legislation. A short account of the way 
in which this form of economic science has come into 
being will indicate more clearly its scope and bearing. 

Just half a century ago, in an inspiriting address ^ 
on " The Progress of Economic Science during the 
Last Thirty Years," William Newmarch summarized 
what he regarded as the greatest achievement of the 
science during the period covered in his survey. 

" Looking back at the changes and the experience 
of which this is a rapid outline, it appears to me that 
I shall not be in any danger of misleading the Sec- 
tion if I suggest that probably the most conspicuous 
and important fact to be found in the history of Eco- 
nomic Science during the last thirty years is this ; 
namely, that while there has been no change in the 
objects to which it is directed — no change in the 
purposes intended to be worked out — while these 
objects and these purposes remain the same in their 
broad and general aspect as they have been from 



^ Newmarch gave the address as President of Section (F) of Eco- 
nomic Science and Statistics of the British Association for the Ad- 
vancement of Science. The address is published in the Journal of 
the Statistical Society, 1861, pp. 451-467. 



Conclusions 171 

the time of Adam Smith, there has been a marked 
change in the Methods according to which Economic 
Science is cultivated. It has ceased to be an abstract 
science, — it has ceased to be a system of subtle and 
ingenious reasonings. It has little by little, and by 
a process cautious and full of promise, become a 
science almost entirely experimental. We have 
learned that in all questions relating to human so- 
ciety — in all controversies where the agency of hu- 
man beings has to be relied upon for working out 
even the smallest results — we have learned that in 
these inquiries the only sound basis on which we 
can found doctrines, and still more the only safe basis 
on which we can erect laws, is not hypothetical de- 
duction, however ingenious and subtle, but conclu- 
sions and reasoning supported by the largest and 
most careful investigation of facts. This vital change 
of method, this substitution of observation and ex- 
periment (and for our present purpose the two words 
mean very much the same thing) for deductions ar- 
rived at by geometrical reasoning, seems to me to be 
the most prominent fact of the last thirty or forty 
years, as regards the progress of the branches of 
knowledge which more immediately interest us in 
this Section." 

The negative attitude of Newmarch with regard to 
theoretical economics I, of course, do not share. The 
quotation has been made in order to stress his point of 
view as to the relation of economic science to legisla- 
tion. The two pervading ideas of the address are. 



172 Laws of Wages 

first, that effective legislation must be based upon ex- 
perience, and, secondly, that experience must be 
interpreted by the statistical method : " we claim for 
Statistics . . . that it is the application of the Exper- 
imental or Baconian method to the several divisions 
of inquiry which relate to man in society. We say 
that where there is no careful application of the 
Statistical method — in other words, where there is 
an absence of observation and experiment, so far as 
observation and experiment can be applied to men 
in Societies — there can be but faint hope of arriving 
at the truth in any line of research connected with 
social problems." ^ 

In the works of Stanley Jevons is found the devel- 
opment of the ideas of Newmarch upon this subject. 
Jevons observed that legislation in England did not 
proceed without what is commonly called statistical 
evidence, but the statistics were not always of the 
right sort, nor were the statistical inquiries always 
conducted according to "true scientific method."^ 
Furthermore, using the hint in Newmarch's address, 
he called the method of legislation he approved 
" Baconian legislation," and he thus described the 
principle upon which it should proceed : " What I 
venture to maintain is that Baconian legislation will 
always proceed by reasoning from the most nearly 
proximate and analogous experience which is avail- 

^ Newmarch: Journal of the Statistical Society, 1861, p. 457. 
2 Essay on "Experimental Legislation and the Drink Traffic." 
Methods of Social Reform, p. 256. 



Conclusions 173 

able. We cannot possibly dispense with general rea- 
soning, hut ive should use it as sparingly as possible. 
We shoidd choose, as it were, the loivest logical elevation 
in sight." ^ 

The part of the quotation that 1 have itahcized 
presents the point of view I should hke to urge. 
According to the argument of the chapter on " Statis- 
tical Laws," the statistical economist proceeds by a 
progressive synthesis from individual facts to general 
facts, and from general facts to statistical laws. He 
expresses the laws in their mathematical form, and, 
where it is possible, he measures the degrees of asso- 
ciation between the related phenomena, expressing 
them as coefficients of correlation, correlation ratios, 
or coefficients of contingency, as the case may be. 
Now in Baconian legislation, the interpretation by 
means of general economic reasoning of the statistical 
laws and coefficients of association constitutes " the 
lowest logical elevation in sight" upon which legisla- 
tion can be effectively based. The practical work of 
the statistical economist bridges the gap between 
general reasoning and the crude facts.^ 

^ Jevons : The State in Relation to Labor, p. 24. 

2 This conception of Statistical Economics, theoretical and applied, 
is receiving a most promising development in the contemporary Italian 
school, whose organ of publication is the Giornale degli Econoniisti. 
Following Professor Pareto's attempt to give concreteness to the theory 
of distribution by basing his reasoning upon a statistical law summar- 
izing approximately the distribution of income in modern societies, 
numerous essays appeared, particularly in Italy, in which Pareto's 
method was applied in the treatment of other social phenomena. Pro- 
fessor Pareto himself, asserting, in 1907, that " the progress of polit- 
ical economy in the future will depend in great part upon the investi- 



174 Laws of Wages 

Coming now to the detailed consideration of the 
practical bearing of the preceding chapters, we may 
observe with reference to the two theories, which for 
the sake of brevity we may refer to as the subsistence 
theory and the standard of life theory, that their per- 
sistence in economic literature gives color to the be- 
lief that wages may be increased in other ways than 
through an increased effective productivity of the 
laboring class. This is particularly true in regard to 
the doctrine of the standard of life, because in sup- 
port of false views, Ricardo's authority may be cited : 
" The friends of humanity cannot but wish that in all 
countries the labouring classes should have a taste for 

gation of empirical laws that are derived from statistics" (Giornale 
degll Economisti, Maggie, 1907, p. 36G), has spent much of his time in 
perfecting the inductive, statistical tool by means of which the em- 
pirical laws are summarized in mathematical form. 

But the formal conception of an Inductive Economics, utilizing as 
means of investigation modern statistical methods, is found in the 
work of Professor Benini and of Professor Bresciaui. In his inaugural 
address as Professor of Statistics in the University of Rome, Professor 
Benini outlined his conception of " Una possibile creazione del metodo 
statistico. L'economia politica induttiva" {Ibid., Gennaio, 1908). 
His volume on Principii di Statistica Metodologica may be regarded as 
his description of the method to be employed in the treatment of this 
aspect of economic science. More recently, Professor Bresciani, in 
his inaugural address as Professor of Statistics in the University of 
Palermo, has treated a phase of the same subject under the title 
" Sul carattere delle leggi statistiche " (Ibid., ]\Iarzo, 1910). In the 
series of articles on correlation and frequency distributions, published 
in 1909, Bresciani has described to his co-workers the methods of Pro- 
fessor Karl Pearson. A marked indication of the influence of this 
constructive group of younger economists is seen in the change in 
the name of their journal. Since 1910, the title of this admirable 
review is no longer simply Giornale deyli Economisti but Giornale degli 
Economisti e Statistica, thus establishing a formal attempt to bring 
theoretical and statistical economics into intimate relation. 



Conclusions 175 

comforts and enjoyments, and tliat they should be 
stimulated by all legal means in their exertions to 
procure them." ^ It is entirely possible with ingenuity 
to interpret Ricardo's meaning from the context so 
that it would seem to be in harmony with the modern 
doctrine, but, without doubt, the vigorous statement 
is both misleading and false : misleading, in conse- 
quence of wrong emphasis in centering attention 
upon increasing wants while ignoring the inevitable 
price of their gratification; and false, in consequence 
of lumping together the " laboring classes," and infer- 
ring that it is true of all grades of labor that there 
should be an artificial stimulation of wants. 

In order to seize the degree of truth in either of the 
two theories that we are considering, it is necessary 
to reason about laborers not as a class that may be 
represented as a whole by a more or less fictitious 
" average laborer," but as made up of groups which, 
in regard to wages, may possibly be subject to differ- 
ent laws or to different degrees of effectiveness in the 
working of the same law. 

If, with this conception, we begin our investigation 
by considering the two theories with reference to their 
relevancy to the groups of skilled and of unskilled 
laborers, we are brought to practical conclusions of 
considerable importance : — 

(1) It cannot be said that in the territory covered 
by our figures the wages of unskilled laborers 

1 Ricardo : Principles of Political Economy and Taxation, McCullochs' 
edit., p. 54. 



176 Laws of Wages 

are determined by the cost of the means of 
subsistence, that is to say, a fixed mode of life. 
This negative statement is a fortiori true of 
the wages of skilled laborers ; 

(2) There is a close correlation between the 

wasfes of unskilled laborers and their stand- 
ard of life, but the correlation is not so high 
as to justify the inference of a cause and 
effect relation ; 

(3) The correlation between the wages of skilled 

and of unskilled laborers is much higher than 
the correlation of the wao;es of unskilled 
laborers with their standard of life. 

These facts, which are inductively established, lead 
to the following reflection : the wages of both skilled 
and of unskilled laborers are determined by other 
causes than the adherence of the laborers to a fixed 
mode of subsistence or to a variable standard of life. 
The chief determining cause is the specific productive 
efficiency of each group, as is illustrated in Chapter 
III : the efficiency of the unskilled group yields a 
wage that affords a variable standard of life, and 
because of the great supply of labor of this character, 
both the wage and the standard of life vary within 
narrow limits. The wages of the skilled group are 
likewise dependent upon the specific productive effi- 
ciency of the skilled group, but, because of the oppor- 
tunity enjoyed by employers in an open market of 
substituting, within limits, unskilled for skilled labor, 



Conclusions 177 

the strategic advantage of skilled laborers is affected 
by the wage received by unskilled laborers, as is in- 
dicated in Chapter IV. It is submitted that these 
facts have a fundamental bearing upon the theory of 
wages, upon the conception of the solidarity of in- 
dustry, and upon all projects having in view the 
bettering of the state of the laboring class by the 
establishment of a legal minimum wage with the 
necessary concomitant regulation of the supply of 
unskilled labor. ^ 

The idea of the solidarity of industry receives in- 
creased illumination from the conclusions of the 
chapter on " Wages and the Productivity of Labor." 
It was there established — 

(1) that average wages increase with the specific 

product of labor ; 

(2) that the more rapid the increase of capital in 

the industry, the more rapidly do wages 
increase ; 

(3) that the fluctuations of wages about their 

general trend are inversely correlated with 
the machine-power with which the laborers 
work. It is true that these points were es- 
tablished only with reference to the one 
industry for which we could obtain adequate 
data, but there is the great satisfaction of 
kjQOwing that the inductive findings with 
regard to this one industry are in complete 

1 Cf. The Minority Report of the English Poor Lmo Commission, 1909. 



178 Laws of Wages 

accord with the conclusions of a priori reason- 
ing. 

The very high coefficients of correlation measuring 
the relation between the variables that figure in these 
three propositions compel the acceptance of the idea 
of solidarity which sympathetic supporters of the 
cause of the laborers too frequently ignore. It is 
clearly indicated that one of the most valuable 
services that can be rendered by labor organizations 
consists in using their power to induce and compel 
the highest possible efficiency of plant and industrial 
organization. The resulting increased productivity 
will supply the fund from which increased wages may 
be obtained, and a permanently increasing wage can 
be secured only by increasing the flow of the specific 
products of labor. 

It has been said that the results of Chapter III 
compel the acceptance of the idea of solidarity of 
industry. It is not useless to add that this does not 
by any means suggest that the present form of soli- 
darity is the best that is conceivable. There is a 
perplexing statement in this connection in Professor 
Clark's Distribution of Wealth : ^ — 

" For nothing, if not to protect property, does the state exist. 
Hence a state which should force a workman to leave behind 
him in the mill property that was his by right of creation, 
would fail at a critical point. A study of distribution settles 
this question, as to whether the modern state is true to its 
principle. Property is protected at the point of its origin, if 
actual wages are the whole product of labor, if interest is the 

1 Page 9. 



Conclusions 179 

product of capital, and if profit is the product of a coordinating 
act." 

When this introductory statement was followed by 
the admirably lucid and cogent proof with which we 
are familiar that each factor in production does) tend 
to get what it produces, one could scarcely avoid 
a sense of baffled enthusiasm in recalling the words 
that have just been quoted. 

Of course the solution of the difficulty lies in the 
apprehension that the introductory statement and the 
argument take for granted the present forms of own- 
ership of property and the present social and technical 
conditions of production. It is entirely conceivable 
that a form of distribution of property which when 
tested by any familiar standard of equity would be 
pronounced inequitable, could coexist with each factor, 
in production tending to get what it produced. The 
social and technical conditions of production might 
cooperate to reduce the national dividend to a mini- 
mum and still that minimum would be distributed 
according to the specific productivity of the several 
factors. 

The same difficulty takes a visible form in the 
treatment of the problem of production and distribu- 
tion by a series of simultaneous equations, as, for 
example, that problem is treated by Professor Mar- 
shall^ and Professor Pareto.^ The problem of distribu- 

1 Marshall : Principles of Economics, 4th edit. Appendix, particu- 
larly notes XTV, XXI. 

^Pareto: Cours d'economie politique. Vol. I, Principes d'e'conomie 
politique pure. 



180 Laws ,of Wages 

tion is shown to be determinate if the following facts 
are known : (1) the effective demand schedules of the 
members of the community, which result from their 
desires and their wealth ; (2) the supply schedules of 
the factors of production, which result from the 
amounts of the factors in existence and the needs and 
dispositions of their possessors ; (3) the functions 
descriptive of the technical conditions of production, 
w^hich depend upon the state of invention and the 
legal and other social conditions under which industry 
is carried on. Whatever may be the character of the 
functions of these three items, it is shown that under 
the hypothesis of least cost or of perfect competition, 
each factor will tend to get what it produces. But 
that fact is not assumed by either Professor Marshall 
or Professor Pareto to be any justification of the par- 
ticular forms that may be assumed by the functions. 

This observation brings us to a perception of the 
further practical bearing of the results of Chapter 
III. In order that the problem of distribution of 
income may be determinate, it is necessary that the 
number of equations in the problem shall be equal to 
the number of unknown quantities. Now a consider- 
able number of the necessary equations are dependent 
upon the proof that under free competition, or the 
hypothesis of least cost, each factor in production 
gets what it produces, and the results of our chapter 
show that so far as labor is concerned this tends to 
be the fact in the present industrial organization of 
society. That is to say, an important part — but 



Conclusions 181 

only a part, let it be understood ^ — of the momentous 
problem of the organization of industry and the dis- 
tribution of income is worked out as it should be in 
the present industrial society. 

This point is of extreme importance, and its signifi- 
cance should not be misunderstood. There are two 
distinct questions ^ in the theory of the socialization 
of the means of production : (1) as to whether it is 
socially expedient for the state to assume control of 
any particular form of the means of production, and 
(2) as to the principles upon which the ministry of 
production in a collectivist state should organize and 
carry on industry with the means of production placed 
at its disposal. Postponing the discussion of the first 
question until we come to the consideration of the 

^ Marshall : Principles of Economics, 4tli edit., p. 588. 

" Subject to conditions which are indicated in the foot-note, but 
are not important for our main purpose, the wages of every class of 
labour tend to be equal to the net product due to the additional 
labour of the marginal labourer of that class. 

" This doctrine has sometimes been put forward as atheory of wages. 
In reply to any such preteusion, it may be objected that the doctrine 
that the earnings of a worker tend to be equal to the net product of 
his work, has by itself no real meaning ; since in order to estimate 
net product, we have to take for granted all the expenses of production 
of the commodity on which he works, other than his own wages. 

" But though this objection is valid against a claim that it contains 
a theory of wages, it is not valid against a claim that the doctrine 
throws into clear light the action of one of the causes that govern 
wages." 

2 In this paragraph, I follow Professor Barone, who, utilizing the 
suggestions of the earlier work of Pareto, has given a mathematical 
demonstration of the proposition under discussion, in his substantial 
articles on ^' II ministro della produzione nello stato collettivisto," 
which were published in the Giornale degli Economisti, 1908, pp. 267- 
293 ; pp. 391-414. 



182 Laws of Wages 

results of another chapter, we may observe that if in 
a collectivist state the minister of production should 
seek to maximize the national dividend of the com- 
munity, he must so apportion the means of production 
that their marginal productivity shall be the same in 
different forms of production, and he must place values 
upon the units of the several factors that are propor- 
tionate to their respective marginal productivities. 
The latter principle of valuation is the principle of 
reward according to specific productivity that tends 
to be realized in the present industrial state. 

In reviewing the results established in the chapter 
on " Wages and Ability," we shall see that they lend 
additional force to what has just been said. I should 
like first, however, to amplify an idea to which refer- 
ence was made a moment ago. In summarizing the 
results of the chapter on " Wages and the Standard 
of Life," the importance of distinguishing in theory 
between the qualities of different groups of laborers 
was dwelt upon. One of the invaluable services that 
the newer statistical methods are likely to render to 
pure economics is to liberate speculation from the 
bondage to the average in which it has labored since 
the beginning of the science. 

The syndicalist Georges Sorel has shown how, 
influenced by the special conditions of production in 
the large manufacturing industries of England and 
by the prevailing forms of physical science, the nine- 
teenth century economists disregarded the qualities 



Conclusions 183 

that differentiate laborer from laborer and conducted 
their reasoning with regard to " units of labor " and 
" laborers of average capacity." 

"On arriva ainsi a penser que, dans I'industrie la plus 
avancee, il devenait inutile de tenir compte des qualites pro- 
pres des hommes et qu'on pouvait considerer les travailleurs 
comme des atomes de qualite moyenne, susceptible d'etre 
seulement distingues par des grandeurs matliematiques, en 
sorte que toute I'economie devint une science des quantites de 
travail raises en jeu par les capitalistes." ^ 

The most marked development of science in the 
latter half of the nineteenth century took its de- 
parture from the study of deviations from the average 
rather than of the average itself, and economists will, 
of course, adjust their theories in the light of this 
newer evolutionary science. There can be little doubt 
that egalitarian doctrines of the past century were 
fostered through the inadequate method of reasoning 
by vaguely conceived averages and the ignoring of 
the law of the natural differences between individuals 
in any large group. 

That there is a law of natural differences between 
individuals in any large group, no one who is ac- 
quainted with the results of recent biometric and 
anthropometric work will deny. The point that con- 
cerns us, however, as practical economists is to know 
whether this law of natural differences finds its ex- 
pression in the actual earnings of laborers. Accord- 
ing to the productivity theory of wages the distribu- 
tion of general wages among the groups making up 

1 Georges Sorel : Introduction a Veconomie moderne, p. 29. 



184 Laws of Wages 

the class of laborers should be according to the pro- 
ductive efficiency of the respective groups. The re- 
sults of our investigation have established that the 
law of the natural difference in ability between 
individual laborers does find its expression in the ap- 
portionment of earnings among laborers in the present 
industrial state, and that, furthermore, the congruence 
is remarkably close between the actual distribution 
of wages and distribution as it should be according to 
a priori theory. 

As a rule, the curve descriptive of the distribution 
of wages among a large group of laborers employed 
in numerous occupations is skew in a positive direc- 
tion. This skewness is generally, but not always, a 
sign of improving conditions in the laboring class. 
When the industry grows more productive and earn- 
ings are such as to justify an increase in Avages, the 
more intelligent and better organized laborers are the 
first to perceive and to take advantage of the improved 
conditions. The more prompt adjustment of wages of 
the abler laborers to the increased productivity gives 
the wages curve a greater measure of skewness. The 
subsequent changes in the degrees of skewness are de- 
pendent upon the degree of friction in the adjustment 
of the wages of the less able laborers and upon the 
improving or declining general conditions of industry. 

In a collectivist state conducted upon the principle 
of rendering a maximum the product of available 
labor and capital, the differences of earned incomes 
of the members of the state must conform to the very 



Conclusions 185 

same law that obtains in the present industrial order. 
It is a mark of the great progress in the scientific 
treatment of social questions that upon this funda- 
mental point economist and socialist are in agreement. 
Writinyi; under the influence of the idea of Marx that 
is quoted as the motto to this chapter, Sorel observes 
" que c'est par un mecanisme emprunte a I'ere capital- 
iste que le socialisme compte regler la repartition," ^ 
and then, touching upon the question before us, he 
says : " Le capitalisme . . . tend a produire une cer- 
taine ^galisation du travail entre les diverses parties 
de I'usine ; mais comme il a besoin d'un nombre con- 
siderable d'hommes particulierement actifs, attentifs 
ou experiment's, il s'ingenie a donner des supplements 
de salaire aux hommes qui lui rendent ainsi plus de 
services ; ce n'est point par des considerations de 
justice qu'il se regie dans ce calcul, mais par la seule 
recherche empirique d'un equilibre regie par les prix. 
Le capitalisme arrive done a resoudre un probleme 
qui semblait insoluble, tant qu'il avait ete etudie par 
les utopistes ; il resout la question de I'^galit' des 
travailleurs, tout en tenant compte des inegalites 
naturelles ou acquises qui se traduisent par des in- 
egalites dans le travail." 

The only " socialist revolution " of which we have 
knowledge is the revolution in the opinions of lead- 
ing "scientific socialists "^ — their abandonment of 

^ Sorel : La Decomposition du Marxisme, p. 44. 

2 The right to refer to Sorel as a socialist can scarcely be denied in 
view of his claim to teaching le Marxisme de Marx. 



186 Laws of Wages 

their doctrine of the cataclysmal destruction of capi- 
talism and their apprehension of the necessity of reg- 
ulating distribution in a collectivist state by means 
of a mechanism borrowed from the capitalist era. 

The most critical practical questions concerning 
the income of laborers are the questions as to the 
effect upon wages of strikes and of the concentration 
of industry in large establishments. It is by means 
of the pressure of labor organizations, which in its 
acute stage takes the form of strikes, that laborers 
expect to compel an increase of wages ; and it is from 
the growing magnitude of the aggregations of capital 
which tend more and more to control the output in 
the market that they expect to find their greatest 
opposition. These two subjects form the topics of 
our last two chapters, the results of which, as to 
their practical bearings, we shall consider in se- 
quence. 

Since the attitude of the public toward industrial 
disputes, in the matter of public sympathy and public 
control, must change with the degree of relevant 
scientific information that is available, it will be 
well to consider our great progress during the last 
half century in the understanding of the nature, 
causes, and effects of strikes. 

Fifty years ago the dominant school of economists 
was united in its insistence upon a vicious, radi- 
cally fallacious doctrine of wages which contained 
as corollaries : — 



Conclusions 187 

(1) the doctrine of the impotence of trades-union- 

ists to increase their wages through combi- 
nations and strikes ; 

(2) the doctrine of the impotence of laborers to 

increase their wages through the increase 
of their productive efficiency ; 

(3) the doctrine of the impotence of laborers to 

better their condition by exerting pressure, 
through combination, upon the employers 
to the end that they should increase the 
efficiency of their plant and organization. 

This theory of wages was so hypothetical and so 
vague that it was impossible to put it to an inductive 
test. Indeed the nebulous character of the theory was 
one condition of its persistence ; for, as soon as pre- 
cision was given to the terms in which it was ex- 
pressed, it was seen that the modicum of truth in 
the doctrine was but little more than a pedantic 
elaboration of a platitude. 

The successful middle class that had risen in wealth 
and power during the period following the industrial 
revolution was predisposed, in consequence of its 
industrial interests, to accept the economic doctrine 
of the wages-fund with all of its corollaries. Accord- 
ingly, strikes and labor combinations were regarded 
as being impotent to achieve the effects sought by 
trades-unionists and as being, moreover, conspiracies 
against public order. In the meanwhile strikes in- 
creased in number and extent and bitterness of con- 



188 Laws of Wages 

flict, and, notwithstanding the enormous pubhc 
interests at stake, no public authority concerned 
itself with the collection of adequate material bear- 
ing upon the origin, causes, and outcome of strikes, 
which material alone, when properly interpreted, 
could possibly afford guidance in the direction and 
control of this form of industrial warfare. 

During the interval of fifty years, the progress in 
the understanding of the labor question has been 
such as to lead to a reversal of attitude upon all of 
these points. A new theory of wages, definite in 
form and admitting of empirical tests, has been 
developed as a part of a general efficiency theory of 
distribution. So far as its fundamental propositions 
have been tested it has been found that the theory 
tends to be realized in actual practice. The essential 
idea of the new doctrine is that, with a definite tech- 
nical and social organization of industry, the laborer 
tends to get what he produces. Corollaries to the 
doctrine are : — 

(1) that whatever leads to an increase in the effi- 

ciency of the worker will tend to increase his 
wages ; 

(2) that if increased wages do not follow upon in- 

creased efficiency of the industrial worker, 
the labor combinations can, through strikes, 
force the cession of the increased product ; 

(3) that without the increased efficiency no amount 

of striking will result in a permanent increase 
of wages ; 



Conclusions 189 

(4) that labor organizations, through their powers 
of putting pressure upon the employer to 
increase the efficiency of his plant and or- 
ganization, have a means not only of in- 
creasing wages, but of enlarging the national 
dividend. 

Pubhc opinion is in the process of adjusting itself 
to the new light. The vagaries of early economists 
have discredited a priori opinions as to industrial 
matters ; it is insisted that economic truths like all 
other truths can be reached only by treating scien- 
tifically the relevant facts that are laboriously accu- 
mulated. Accordingly, in nearly all of the states of 
Europe, public bureaus have been established for the 
purpose of collecting and interpreting the facts bear- 
ing upon the labor question. 

The material available at present is neither satis- 
factory in classification nor adequate in amount for 
a complete treatment of the question of strikes. But 
the results in Chapter Y show — 

(1) that the outcome of strikes is subject to statisti- 

cal and economic laws ; 

(2) that the scientific apparatus in the form of 

economic theory and statistical mathematics 
has been developed to such a degree of power 
as to be equal to the handling of this com- 
plex problem ; 

(3) that there is reason for beheving that if data 

of satisfactory quality and quantity were 



190 Laws of Wages 

supplied, the whole subject could be placed 
upon a scientific foundation admitting of the 
prediction of average results in a way that 
would approximate the actuarial calculations 
of life insurance. 

Public opinion, as has been said, is adjusting itself 
to the newer light. Public opinion is unalterable in its 
condemnation of the form of industrial treason that 
is manifested in a general strike. Its condemnation 
is unalterable because there is absolute certainty that 
no economic service rendered by the aggrieved class 
is comparable to the economic loss that would follow 
upon a tolerated general strike. Public opinion is in 
sympathy with or in opposition to strikers according 
as it is made clear that the strikers have or have not 
created a value that is appropriated by the employer. 
It would therefore seem obvious that since public 
opinion does utilize the degree of knowledge that is 
available, and since adequate scientific knowledge 
could be supplied, if only the facts were properly 
collected and analyzed, we should not be far from the 
solution of a problem that many have regarded as in- 
soluble. Our progress during the last fifty years 
justifies this belief ; the importance of the question 
justifies the exertion of any degree of pressure upon 
an industrial group that should either withhold the 
facts, or pollute the sources of knowledge for the 
purpose of exploiting an opportunity created by public 
ignorance or misinformation. 



Conclusions 191 

In the matter of the attitude of the state toward 
economic activities, we have made the distinction ^ 
between the question (1) as to what forms of capital 
should be socialized, and (2) as to the principles that 
must be followed by a collectivist minister in the direc- 
tion of production and distribution. With regard to 
the latter question it has been shown to be demonstrable 
that, if a collectivist state is to have any degree of 
stability, the principles followed in the apportionment 
of labor and capital in production and in the distri- 
bution of the product of industry must be the same 
in the collectivist state as in the present industrial 
state, and that when recent socialist thinkers have 
attempted to give definiteness to their proposals for 
collective control and administration, they admit this 
fact. We have further shown that when competition 
tends to be realized — in the technical sense of the 
word competition — or when through collective bar- 
gaining results approximating competitive standards 
are reached, the presumption is against any attempt 
at socialization of the industry concerned. 

The results of Chapter VI on " Wages and the 
Concentration of Industry" will throw some light 
on the first of the two questions into which we 
have divided the problem of socialization ; viz., what 
forms of capital should be socialized. As we have 
shown that the presumption is in favor of the present 
order of production when competitive standards are 

1 Barone made the distinction in 1908 in his articles on " II mi- 
nistro della produzione nello stato collettivisto." 



192 Laws of Wages 

realized, it is quite clear that the ground for belief in 
the expediency of socializing any form of concentrated 
industry must be found in the deviation of the facts 
of industry where concentration obtains from the 
standards that would be realized under competitive 
conditions. We are therefore led to inquire in what 
respect, so far as the laborer is concerned, do the 
facts of industry where masses of capital and labor 
are aggregated differ from the facts where labor and 
capital cooperate in the same industry upon a smaller 
scale. Concentration of industry, in the sense in 
which the term is used here, viz., of aggregation of 
capital and labor in the same establishment, does not 
by any means imply the abrogation of competition. 
But it is a normal form of transition from competi- 
tion to monopoly and for that reason deserves especial 
investigation. 

The researches of Chapter VI have been under- 
taken with a view to discovering the effects of con- 
centration of industry upon the status of the laborer. 
The broad general results of the chapter are ^ — 

' A technical detail affecting the comparison of the wages received 
in large and in small establishments is of sufficient importance to 
justify a note. 

When such comparisons are made, spurious differences that are 
due to several causes are obtained. A common form of spurious dif- 
ferences has its origin in the lumping together of wage statistics from 
different geographical districts, as, for example, when the wages paid 
in the manufacture of cotton in the northern and southern states of 
the United States are massed in a classification of rates of wages ac- 
cording to the size of establishments (cf. Earning.<< of Wage-earners, 
Census of Manufactures, 1905, Bulletin 93, pp. 73-81). In this case, 
a comparison between the mean rate of wages in large establishments 



Conclusions 193 

(1) That as regards the four critical items — rate 

of wages, amount of employment, continuity 
of employment, and length of the working 
day, the status of the laborer improves with 
the increasing concentration of industry ; 

(2) That the greater complexity of production fol- 

lowing upon the concentration of labor and 
capital creates new opportunities for efficient 
laborers to exploit their differential ability ; 

(3) That, when the degree of the concentration of 

industry increases, the similarity and the 
differences in the operation of the law of 
the variation of wages with the age of the 

and the mean rate in small establishments would show a difference 
in favor of large establishments. But this difference would be spu- 
rious so far as concerns the effect of the size of the establishment 
upon the rate of wages. The fact that the large establishments are 
situated in greater number in the northern states where a high rate 
of wages prevails would be an explanation of a difference in the rate 
of wages paid in the large and in the small establishments. 

A more subtle form of spurious difference is manifested when 
wage statistics are presented without reference to the age grouping of 
the laborers. That is to say, increasing concentration of industry 
implies a form of industrial selection of laborers which shows itself, 
in one way, by the different age groupings of laborers in large and in 
small establishments. 

The constants in the equation expressing the law of the variation 
of wages with age vary not only with the degrees of concentration of 
capital and labor in the same industry but also from industry to in- 
dustry. In both cases these variations should be taken into account 
before comparisons are instituted between the rates of wages in dif- 
ferent industries and in establishments varying in size in the same 
industry. It is suggested that in the presentation of wage statistics 
a plan should be followed similar to the procedure of the English 
Registrar General, in his comparison of death rates in different places 
where the age groupings of the populations are different. 



194 Laws of Wages 

worker are explicable by means of the 
hypothesis that the laborer tends to earn 
an income proportionate to his efficiency in 
production. 

These inductive findings not only reenforce the 
belief that, so far as the welfare of the laborer is con- 
cerned, concentration of industry is no ground for 
the socialization of industry, but they place in clearer 
light the solidarity of industry and illustrate how the 
increasing welfare of the laborer is dependent upon 
the skillful management of large capital. 

We finally reach our question as to what forms of 
capital or economic institutions should be socialized, 
meaning by socialization the administration in the 
common interest of society. We need a principle 
upon which to make the decision, and we need a 
method by which each institution may be put to the 
test of our principle. 

In our quest of a principle we may start from two 
propositions which I think will be accepted by both 
economist and socialist. We may assume first, that, 
so far as it is compatible with the acquisition of 
better things, it is desirable to have the national 
dividend of wealth a maximum ; and, secondly, that 
those who take part in the creation of the dividend 
should receive shares that are proportionate to their 
contribution to the total product. Our principle is 
implicit in these propositions, and it may be worded 
as follows : the economic resources of a state should 



Conclusions 195 

be so utilized as to render the national dividend of 
wealth the maximum that is compatible with the 
acquisition of better things, and the dividend should 
be so distributed that each contributor to its pro- 
duction should receive a share proportionate to his 
services. 

The method of applying this test of an efficient 
economy is a combination of synthetic economics ^ 
and statistical economics. We have shown in an 
earlier part of this chapter that, according to recent 
economic theory, the problem of production and dis- 
tribution of wealth is determinate, if we admit the 
hypothesis of least cost or of perfect competition and 
have a knowledge of three facts : (1) the effective 
demand schedules of the members of the community, 
which result from their desires and their wealth ; 
(2) the supply schedules of the factors in production, 
which result from the amounts of the factors in 
existence and the needs and dispositions of their 
possessors ; (3) the functions descriptive of the 
technical conditions of production, which are depend- 
ent upon the state of invention and the legal and 
other social conditions under which industry is carried 
on. Starting from this hypothesis and the knowledge 
of these three facts, it may be proved that under the 
assumed conditions the national dividend is a maximum 
and the owners of the factors of ^^^oduction are re- 

1 Barone refers to the type of economic theory in which the conditions 
of production and distribution are simultaneously presented in a 
series of equations as L'economia sintetica. 



196 Laws of Wages 

warded ivith shares jproioortionate to the contributions 
of the several factors to the production of the dividend. 
The words that are italicized in the preceding de- 
scription are critical for the application of the test of 
an efficient economy. The test requires that the re- 
sources of the state shall be so utilized as to render 
the national dividend the maximum that is compatible 
with the acquisition of better things, whereas in the 
above economy, the national dividend is rendered a 
maximum under the assumed rights of ownership of 
the factors of production and the existing technical, 
legal, and other social conditions of production. 
Furthermore, the test requires that the individuals in 
the community should receive shares of the dividend 
proportionate to their contributions in its production, 
whereas the above economy cedes to the owners of 
the factors of production shares proportionate to the 
contributions of the factors. Whether, in these two 
points, there is a great or small discrepancy between 
the ideal and the actual depends upon the concrete 
form of the premises upon which the theory rests. 
It is the task of synthetic economics to supply a 
general solution of the problem as to the effects upon 
the size of the national dividend and its resulting 
distribution of any alteration in the hypotheses or the 
premises upon which the theory rests. It is the task 
of statistical economics to give concrete form to the 
premises and the general solution by summarizing in 
mathematical form the relevant facts in the present 
order of production and distribution. 



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which enter into the complex economic life of the nation. A 
young man who wishes to read even the daily paper with full in- 
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ployed for the help which it would give him in understanding 
current discussions of such topics as the standard of living ; the 
natural resources of the country and their conservation ; the 
relations of labor and immigration ; of the labor of women and 
children to industrial progress ; of organization in business and 
its tendencies ; of the growth and functions of large corporations ; 
of public ownership ; of the various experiments which have been 
tried at different times, or the programmes which social leaders 
are now proposing for the remedy or the prevention of economic 
injustice. 

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Law for the American Farmer 

By JOHN B. GREEN, of the New York Bar 

Decorated cloth, xvi -\- 438 pp., i?idex, $1.50 net; by tttail, $1.63 

" A volume that bears the marks of painstaking effort to present 
information that will be useful to those engaged in agriculture. 
In no sense is the book intended to take the place of counsel, 
but merely to fit the owner of a farm to cope with legal ques- 
tions which may arise any day in the conduct of his farm. 
Any person who will make himself famihar with the contents 
of this book will possess a liberal education." — Boston Globe. 

A Living Wage : its Ethical and Economic Aspects 

By Rev. J. A. RYAN. Cloth, \2mo, $1.00 7iet ; by mail, $1.12 
" A clear and concise study of the wage problem," 

The Labor Movement in America 

By RICHARD T. ELY. \2mo, half leather, $1.25 net 

A historical and critical sketch of the struggle of the day-by- 
day working population of North America for the betterment 
of their condition. 

Labor Problems 

By THOMAS S. ADAMS and HELEN L. SUMNER 

2>vo, cloth, gilt top, $1.60 Jiet 
" Invaluable as presenting in convenient and accessible form 
necessary material that would else have to be searched for in 
widely scattered sources." — Providence Journal. 

Federal Power over Carriers and Corporations : 

A Study of the Sherman Anti-Trust Law 

By E. PARMALEE PRENTICE. \2mo, cloth, $1.50 net 

This is an exhaustive study of the Sherman Anti-Trust Act 
and of the Federal powers upon which the Act is based. 



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Wage-Earning Women 

By ANNIE MARION MacLEAN 

Professor of Sociology in Adelphi College 

Cloth, leather hack, i2mo, $1.25 net; by mail, $1.35 

"This book needed to be written. Society has to be re- 
minded that the prime function of women must ever be 
the perpetuation of the race. It can be so reminded only 
by a startUng presentation of the woman who is ' speeded 
up ' on a machine, the woman who breaks records in pack- 
ing prunes or picking hops, the woman who outdoes all 
others in vamping shoes or spooling cotton. . . . The chap- 
ters give glimpses of women wage-earners as they toil in dif- 
ferent parts of the country. The author visited the shoe- 
shops, and the paper, cotton, and woollen mills of New 
England, the department stores of Chicago, the garment- 
makers' homes in New York, the silk mills and potteries 
of New Jersey, the fruit farms of California, the coal fields 
of Pennsylvania, and the hop industries of Oregon. The 
author calls for legislation regardless of constitutional 
quibble, for a shorter work-day, a higher wage, the estab- 
lishment of residential clubs, the closer cooperation between 
existing organizations for industrial betterment." 

— Boston Advertiser. 

Making Both Ends Meet : 

The Income and Outlay of Ne<zu York Working Girts 
By sue AINSLIE CLARK and EDITH WYATT 

Illustrated, cloth, i2mo, 270 pages, $1.50 net; by mail, $1.60 

The girl who, without friends or home, is obliged to earn 
her living in a big city, faces a very real problem. Vari- 
ous phases of this problem have been dealt with by phil- 
anthropic, social and religious workers and writers, but 
the solution is seemingly as far away as ever. Though 
there are many homes and organizations of a semi-chari- 
table nature in all our large cities, these really can care for 
and watch over but a small per cent of the working girl 
population. Those who for one reason or another do not 
come within the radius of these institutions must shift en- 
tirely for themselves. These are the subjects of Mrs. 
Clark and Miss Wyatt's book. 



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Publishers 64-66 Fifth Avenue New York 



American Social Progress Series 

Edited by 
Professor SAMUEL McCUNE LINDSAY, Ph.D., LL.D., 

Columbia University 



A series of handbooks for the student and general reader, giving 
the results of the newer social thought and of recent scientific in- 
vestigations of the facts of American social life and institutions. 
Each volume about 200 pages. 

1 — The New Basis of Civilization. By Simon N. Patten, Ph.D., 

LL.D., University of Pennsylvania. Price, $1.00 net. 

2 — Standards of Public Morality. By Arthur Twining Had- 

LEY, Ph.D., LL.D., President of Yale University. Frice, 

^i.oo net. 

3 — Misery and Its Causes. By Edward. T. Devine, Ph.D., 

LL.D., Columbia University. Price, $1.2^ net. 

4 — Government Action for Social Welfare. By Jeremiah W. 

Jenks, Ph.D., LL.D., Cornell University. Frice, $1.00 net. 

5 — Social Insurance. A Program of Social Reform. By Henry 

Rogers Seager, Ph.D., Columbia University. Frice, $1.00 
net. 

6 — The Social Basis of Religion, By Simon N. Patten, Ph.D., 

LL.D., University of Pennsylvania. Frice, $1.25 net. 

7 — Social Reform and the Constitution. By Frank J. Goodnow, 

LL.D., Columbia University. Cloth, i2mo, ^1.50 net. 



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